Different builds, and what to chose

Flash
I like to go with this since it can be great for both chasing and escaping dangerous situations. It allows you to do the "Triple Flash" With flashing to a minions using Crescent Strike (Q) on it and then Lunar Rush two times in a row

- Moonsilver Blade

Diana has increased Attack Speed. Every third strike cleaves nearby enemies for additional magic damage.

I don't know other peoples opinion on this passive but i find it really strong, with low AP and high attack speed you will be able to do like 300 damage each 1.5 sec which is an major damage increase.

Effective use

I get a lot of attack speed to actually do a lot of damage with this passive and i think it's way to strong

- Crescent Strike

Diana swings her blade to unleash a bolt of lunar energy, afflicting enemies with Moonlight and dealing damage in an arc before exploding.

This is your main damage ability and should be used on enemies when able too, with low CD and low mana cost.

Effective use

Try to hit as many people as possible with it, it can also be used a an scouting tool to actually check if there is danger ahead since it reveals enemies.

- Pale Cascade

Diana creates three orbiting spheres that detonate on contact with enemies to deal damage in an area. She also gains a temporary shield that absorbs damage. This shield is refreshed if all three spheres detonate.

This is your defensive shield which actually also deals quite an amount of damage

Effetive use

To maximize the amount of shield you get you should damage people with the orbs flying around you, and if you want to get the damage from the shield or the quick refresh on the shield you can use your E ( Moonfall to get enemy champs right to you

- Moonfall

Diana draws in and slows all nearby enemies.

Your slowing ability and your aoe "knocback" when you're ganking, it drags all enemies to you,

Effetive use

To use your Moonfall effective try to wait with using it when you're ganking until after the person you're ganking have used they escape mechanism and then drag them to you and active your W and hit your Q for some extra damage and for the ability to use your double ult.

- Lunar Rush

Diana teleports to an enemy and deals magic damage. Lunar Rush has no cooldown when used to teleport to a target afflicted with Moonlight.

A really good, low CD, low cost "flash" ult, which can be used for almost everything. It deals decent damage and since it can be used twice (if you hit your Q) it can be used for tower diving and jumping to a minion after

Effective use

To maximize the effect of this hit your Q Crescent Strike before using ult to do a double flash, but it can also be used for juking and jumping to creeps by either placing a ward and ult or Q to get vision (on either minions or champions) and then ult.

Starting items

This section is taken from Apotheosis Guide to Tryn with his permission of course :)

Warding is way too over looked by many teams. I'm going to show you how to ward correctly, or at least how my team and I ward. The ward possibilities are obviously endless for 5s. These are the primary areas that you and your team will be warding each and every game.

Order of priority; Use Sight Ward and Vision Ward where necessary:

Baron/Dragon Wards:
However you decide to set these up with your team, whether it be orderly among the team or supports only buy wards, make sure these are always laid out! Baron and Dragon are what we're primarily keeping an eye on here. Early in the match it's not as important obviously, however, you still need to know whether top, mid, or bot will be set up for a gank when enemy laners/junglers are wandering about. These early kills can help the enemy sculpt the rest of the match and land a victory. We don't want to be allowing the enemy to kill either Baron or Dragon. That's a good chunk of gold that will distribute among their team, not to mention Baron's handy buff. Again, don't overlook these wards!

Note: I would recommend using Vision Ward for these locations, especially Baron mid-late game. If not Vision Ward, then make sure someone, usually the tank, has Oracle's Elixir for discovering enemy wards.

Self Privacy Wards:
There's orange points at top, mid, and bot hiding locations. I would hope that your entire team would try to ward the areas entitled to them. These wards are not entirely important, however, they are lifesavers. Junglers and wandering laners will use these bushes to set up for early kills. If you're pushing your lane, then it would be a good idea to ward the bush(s) that is closet to you.

Team Privacy Wards:
These are crucial wards to put out when the match can go either way by eliminating possible ambushes when pushing minions or entering your own jungle.

Game Changing Wards:
Of course all of the wards posted on the map are capable of changing the outcome of a game, but these wards are placed in a location that both teams will always drift by. Reasons to go through the wards (for both teams): Getting to Baron and dragon, changing lanes, shifting from allied jungle to the enemy's jungle (either by self or team) to steal mobs/buffs, shifting as a team to gank the enemy team, etc. If you just have a ward on either Baron and/or dragon, you can still miss the enemy slipping by into your jungle never knowing it. This allows enemies to set up ganks. Therefore, these wards change the outcome of a game because you know whats coming.

Invading Wards:
I thought it was appropriate to name these wards in this manner because you can enter their bushes knowing whether they're there or not before you attempt to set up a gank. The enemy usually walks through these bushes hoping to freely enter their jungle for experience/gold and/or buffs.

Buff Wards:
Monitor your's and enemy's buffs with these wards. Good to set in your own jungle if they start playing dirty and snatching buffs early game from your jungle. These wards are primarily for the junglers of each team.