Jayce is a very versatile champion. He has the ability to close gaps or escape at will. Jayce can be played with multiple different play styles. He can play as a straight AD champion, Tanky AD, or Bruiser AD. Each style has its benefits and weaknesses.

As straight AD he deals massive damage in a short period of time but, if Jayce is stunned or snared he is very squishy.

As Tanky AD he does much less damage but becomes a lot harder to kill which keeps you alive to speed up the team, slow enemies, or knock an enemy back into the fight.

With Bruiser AD it takes the damage from straight AD and the survive ability from Tanky AD and puts them together. All three of these are viable tactics to use for Jayce. This build can also be used to jungle.

Pros + Lots of CC. + Very Mobile. + Can switch between Ranged and Melee.

Cons -Mana trouble. -Stuns/snares counter mobility. -Short range.

Teamwork is an important concept for any champion and Jayce makes an excellent addition to any team. Using his abilities you can knock back enemy champions to the fight, slow ranged trying to escape, speed up a gank, or even speed out of one.
When playing as Jayce using his in Mercury Cannon stance Jayce can do one of three things for your team. The first is shooting through the into the enemy group to take a chunk out of their health. The second thing, which is usually at the same time, is having your team run in through the gate to initiate a team fight. Finally, could be used for is for an escape. This could be as simple as leaving the fight briefly and switching back to ranged, or it could be leaving the fight completely to survive from a bad fight. If trying to escape, works well with .
When in Jayce's melee stance he has another two forms of CC. The first is his . This is very good against slowing a squishy champion so that the team can focus them down without the fear of them escaping. This can also be used in conjunction with to knock that target back into the fight. The way to do this efficiently is to use on an enemy champion, that is on the opposite side of where you want to knock back the focused champion, but making sure the aoe from still hits the focused champion. Once you land and slow them target the champion your team is focusing and use to knock them toward your team. If you are playing straight ad and are squishy you may want to immediately use the escape technique previously mentioned.

By using these techniques Jayce becomes a very important addition to any team configuration.

Makes ganking or escaping an easy feat by flashing over walls or out of reach.
Gives the much needed attack speed to the Bruiser and Tanky build.
By using Ignite you can insure kills from escaping enemies. Ignite also is useful for champions that have too much life steal such as Sion when he uses his ult.
is interchangeable with flash as an escape tool which will make you unable to be caught when combined with Thundering Blow / Acceleration Gate and Mercury Cannon / Mercury Hammer.
This is a must if jungling to take down creep camps with ease.

This is an unfinished guide in reference to reasons why I picked the choices I made. This will come soon, but I wanted to get at least the build out now.