This guide started out when I questioned, "Okay what happens after the Laning Phase?" and no one could answer it. I played a number of games where teams seemed confused as to what the game's priorities were. After watching tournaments, pro streamers, my own games, and friends games I started to dissect what made a team successful at certain points in the game and what made a team unsuccessful. While doing this I was able to simplify the strategy of the game into these Phases that I've written out for you. League of Legends is no more then a large Chess game and I promise if you're team follows these priorities, suggestions, and keeps in mind the things I've illustrated you will have an easier time winning games AND, more importantly, bringing your team on the same page of thought.
Originally I wanted to develop this into a book for Riot to sell, however I never heard back from them, so now It's posted for free.
I will try to keep up-to-date with this guide as the Meta does change, infact, after reading the guide check out my WildCard Ezreal guide and how it can affect the Champion Select Phase.
Enjoy and please let me know if this has helped your team in any way.
Overall, this guide is more for New Players and (for lack of a better term) really bad players. I don't claim to be an brilliantly amazing player but I do feel I know a certain level of strategy. I hope you Enjoy!

This Phase is a series of complex paper-rock-scissors selection between both teams. The team that chooses first is the blue team.

Priorities:
•Developing a team composition (A Deck): Will your team excel in 5v5 team fights, Mobility, Poke, Tankability, Crowd Control, etc.
•Map out the first couple of minutes of your game.

Keep in Mind:
•What side of the map you are playing on because it could alter the advantage your character(s) have in a lane (example: Caitlyn’s snap traps have a slightly stronger advantage for preventing ganks when she is on the blue team as the enemy Jungler will gank the lane in a pretty consistent pathway)
•What bans have been made before the start of selection: are there any champions that you or your team could play that would excel with the removal of such champions.
•What Deck is the other team developing throughout the picking process and are there any weaknesses in the overall team composition.
•You will have a lane that will be counter picked. Analyze who in your team needs to excel quickly, and who can make a later game comeback.
•Invade Potential
•Jungler’s Excel Phase

Position picking: If playing as the purple team (second pick) it is of course best to open with a counter pick of the other team. Your second pick should either be your Jungler or Support. If your opponent opened with their ADC or Support, your first two picks should be your ADC and Support, otherwise, you should counter pick the lane and pick up a Jungler that will easily support that lane. If uncertain of the position of the enemy Blue team’s first pick, your first picks should be both your Jungler and Support. Pick the most confident Jungle champion you have and the most versatile Support champion you have. If playing as the Blue team (first pick) it is best to open with a non-specific champion that could fit multiple roles. This will create confusion and “bait out” counter picks, allowing the rest of your team to counter pick lanes.

This phase is specific to the first two to three minutes of the game. Weather invading or starting at your Home Jungle it is important for your team to remain together. During this phase the team that is together will stay alive, or better, gain first blood and a creep or two is worth missing for that.

Priorities:
•Togetherness: the team that is together will have the best advantage

Keep in Mind:
•Do your opponents have a strong Invade Potential? If so, it might be worth having a ward, or wide placement to see incoming enemies.

Tricks of the Trade: If your opponents have a strong Invade Potential and do invade. You can balance out the loss by quickly invading the enemies Jungle.

This phase sets the tone for the game. Players will harass, gank, level up and develop their Creep Score (CS) to gain the advantage over the lane.

Priorities:
•Creep score: without any kills or deaths the only difference your lane can make is by gaining more gold through CS.
•Leveling: The longer you can safely maintain in your lane the faster you will level, hopefully gaining an advantage over the lane.

Keep in Mind:
•Your opponent has a champion that is roaming the jungle: If you are winning the lane and pushing, investing in some wards will protect you when you are over extended.

Jungler’s Excel Phase: The Laning Phase is the Highest Opportunity Phase for most Junglers. The Jungler should be keeping a close eye on opportunities. Some Junglers do not develop good ganking capabilities until later levels. Recognize this and play passively if needed, to extend the Laning Phase as long as possible. It is also very worthwhile for the Jungler to carry wards, as the Jungler he is second most responsible for warding as he is most equipped to ward in many different areas. This will also help prevent Counter Ganks.

This phase starts generally* when the first turret goes down in any of the lanes and a champion has more freedom to roam and assist with small skirmishes, ganks, and taking objectives like Dragon.

Priorities:
• Taking and maintaining control of Dragon, which is on a six minute timer.
• Taking turrets to gain map control.
• Capturing enemies Out of Position and collecting kills and assists gold.
Keep in Mind:
• Wards are most crucial in this phase as there is a lot of movement through the Fog of War.
• CS should NOT be your priority but it should be maintained, even at a slower rate. The jungle should be available at this phase to collect some small CS.

Tricks of the Trade: The objective phase is a great opportunity for trades or even better. When one of your objectives is going down and there is little your team can do, it could be beneficial to take advantage of the enemy team that is across the map from other objectives. Another technique is taking advantage of Push Bait (example: Wukong has won his lane at top and took the first Tower during his Laning Phase, knowing that dragon will be spawning soon he pushes top lane hard to the next turret, with proper ward coverage, baiting the enemy team to do a multiple man gank, freeing up Dragon for the rest of your teammates).

This phase is not specific to order but generally would follow the Objective Phase. During this phase taking the first Baron Buff can decide a close game, turn around a losing game, or secure a winning game.
Priorities:
• Killing or preventing the killing of Baron Nashor.

Keep in Mind:
• Baron is a crucial aspect of many games: it is wise to have consistent ward coverage so you know when the enemy is trying for Baron.
• Your enemy might have warded Baron as well: An Oracles or Vision Ward will clear the enemy’s vision of what you are doing, however they will see that you have gone to Baron.
• Ward the surrounding area: the enemy will rarely ever simply give your team Baron Buff, wards will allow you to properly disengage if the enemy team is charging at you, fully loaded.

Tricks of the Trade: Baron Steals! Your Jungler should* have Smite as a Summoner Spell and I carefully timed Flash could put the last hit on Baron, giving the rest of your team the Baron Buff.

This phase is usually split into two different perspectives, Offensive and Defensive. And has different priorities based on what position your team is in.
Priorities:
Defensive

• Creep Score: at this point and perspective in the game it is important to gain as much gold as possible to catch up.
• Protecting Turrets/Inhibitors: It can be extremely difficult to win a team fight without the support of your minions and turrets, hang on to them as best as you can.
• Survival: Dying can put you out of the game for close to a minute in this phase, missing out on more CS, and giving openings to your enemies.
• Wards: Keeping wards just outside of your base provide the intelligence to rotate promptly and properly.

Offensive
• Leader Comms: decide which player will make the calls, and follow their calls, quick rotations, and split second decisions can lead to taking an inhibitor, or losing a teammate.

Keep in Mind:
General

• Baron Nashor: Baron Buff might not be necessary for the winning team but leaving it open can provide windows of opportunity for the losing team to make a comeback.
• With just one inhibitor down, every minion for the “winning” team gains health stats. So every lane gains an advantage.
• When three inhibitors are down, each lane now spawns TWO super minions instead of one.

Defensive

• Jungle: If you have the means to ward your jungle, secretly farming the jungle can get you an unseen advantage.

Offensive

• Jungle: farming the jungle can actually waste time and put your teammates at a disadvantage during teamfights.

Tricks of the Trade:
Defensive

• There are some champions that are adapted to Back Dooring (BD). Using these champions to sneak through the jungle and slowly take down enemy turrets and inhibitors can slowly turn your game around (for example: Rengar takes a few wards and sneaks to his enemy’s top inhibitor tower. While a team fight opens at his base he has a safe opportunity to take out the tower and the inhibitor, which relieves pressure on top lane.) This technique is often frowned upon but “All is Fair in Love and War.”

Offensive

• Instead of farming the enemy’s jungle, diminishing it to one small creep at each camp can ensure no additional income for them to sneak while your team is recalling/shopping/respawning.

This phase normally is secured by one team or the other but small factors could* still change the tides. The End Phase generally* is entered once a third inhibitor goes down on either team.
Priorities:

Defensive

• Creep Score: farming is the only thing you can do right now, and is crucial as the enemy minions are strong enough to win the game on their own (This is popularly referred to as “Winions”). Farm for gold and survival.
• Nexus Turrets: Now, the Nexus Turrets are your last line of defense, losing these open your nexus to vulnerability. If possible*, it is worthwhile to even tank damage from minions to spare the turrets any damage.

Offensive

• Safety: The game is theoretically* won, doing something stupid can be a remorseful mistake.
• Quarantine: With three inhibitors down, your minions can win the game. Keep the enemy team away from them and make sure none of your opponents have left the base to possibly make a last ditch effort to Back Door.

Tricks of the Trade: Holding out in the end phase and baiting out one bad initiates from overly cocky opponents can provide an opening for your team to rush the enemy Nexus while one or two players stay on defense. During this phase, enemy’s respawn time can reach up to and possibly over 60 seconds, more than enough time.

Thanks for reading, I hope this could help you and/or your team to do better and transition throughout the game more smoothly.
I have already ran into some hazing comments about this guide. I'm more then welcome to ideas and collaboration to make this guide more solid and accurate. The ideas I have put together are in fact theoretical but any strategy is theoretical when first developed. So work with your team try to follow these guidelines and let me know what you feel works and doesn't work, I'd love the input :)

Thanks you guys and I hope you enjoy the guidelines. Again, you can also check out my individual build guides for Ezreal in every position. I'm trying to develop them more and more with coding but the items, and the R&M are there with a brief description, as well as an explanation of what WildCard Ezreal can do for your Champion Select Phase :)

Enjoy!