Pros:
Really high burst all game.
Consistent poke damage in lane with auto Q
Scales very well
Lots of self peel
Extremely mobile
Different build path for different styles
Extremely fun to play
Cutest girl in league :D

Cons:
Mechanical
Different team fighting then other adc (explained in team fight section.)
no cc to peel off fed dives (yi, tryndamere, etc)

The secondary runes are universal. You need biscuits to sustain your auto q poke in lane.
The primary tree you can go PTA or Conquerer.
PTA gives you more burst in lane, as your full combo procs the PTA very fast, and allows you and your support to burst the other adc.
Conauere gives you more sustain damage mid and late game, as it heals you and helps you stay alive in 1v1 and big fights.
I prefer PTA to burst in lane, but it is ultimately up to you.

There are two important combos to Kaisa: The auto Q combo and the Full burst combo.

Auto Q combo:
This combo is autoing the enemy, and immediately pressing q before backing off. If done right, this will hide the auto animation, and get off a lot of damage in a short time. It takes a lot of practice, so try in in practice tool first. This is mostused in lane to punish on cs, but is also useful in midgame 1v1s to get off a bit more damage.

Full burst combo:
The full burst combo is "Auto W auto Q auto". This will give you five stacks, and proc your passive. It sounds a lot harder than it is. You have to make sure to auto, and immidiatly WQ the target. Kaisa will automatically auto while Q. After the combo ended, make sure to slap the other guy with a auto to set off the passive. If sone right, his can essancially one shot someone below 60-70% health.

In lane your win condition is your passive. If you proc it, you are gonna kill someone. If you don't, then you will lose the trade. Thus W is very important. Hit is and you can in a trade. If you miss it, baile immediately.

In 2v2s, you normally focus whoever your W hits. If your w hit squishy support, then you can kill him. If it hits a tanky support like leona or ali, do the combo and back off. If it hits the adc, then commit and go all in on them.

There are two modes of teamfight for kaisa. The Normal mode, and the hit backline mode.

In normal mode, you need to make sure you are attacking the closest target, all while kiting back and autoing from your max range. This is your default condition in teamfight.

if you want to dive backline, you need to first work out how many CC spells they have. Im talking aboug big slows, stuns, and roots. Things such as ornn R, Mawfite R, Nasus wither, etc. If you wait all of these out, you can go on the back line and fire at will. You can also go if they ahve one spell left. You just need to be mentaly prepaired to QSS or dodge it if it comes. The main idea is, only dive if you know there are no cc that can kill you. If there are cc, you must have a way to beat it, such as qss, or zonia just as mawfite is about to R you.

The core items give you two options. If you are snowballing and know 100% you will go Ad kai'sa, buy stormrazor. This will give you early QE evolve with your rageblade. If you don't know if you want to go Ap or Ad, or is just going even, then go Manamune. It is overall safer and cheaper option.

AD Build :
Ad Build is good if you like to auto-attack to do damage. The build can change into defensive items after hurricane, but i usually max damage with IE a BT. This is because Kaisa have so much peel with invis and R that you don't need a GA. Buf if you are in a tough game, feel free to pick up whatever defensive item you need.

AP Build:
Ap build does damage when your passive procs. This build is based around the dive backline playstyle. It take much more mechanical skill and experiance to play. You need to know exactly how much damage you need to kill someone. The build center around the Nashers, ad it gives you so much damage with W E evolve. The rest of the items are optional based on preference.

Jungle:
Jungle Kaisa is weak early,but have great counter ganks and scaling. If you want to go Ad kaisa, build warrior and rage blade and core, and pick your AD items.
If you want AP, go blood razor and rage blade, and pick your Ap Items.