This is w***up, Zil is the booomb. He's gonna mess your day up.

Pros:
Amazing harasser
Revives champs
You will most likely be able to use his ulti twice in a battle (late game)
Gives the entire team 8% more xp gain
Nice range
Mad assists
Cons:
Very vulnerable when silenced
Small damage output on champs with magic resistance
Ulti requires a lot of backwatching
Jungling is very dangerous

I like to play with teleport and clarity.
Clarity will allow you and your lane partner to spam spam skills left and right, keeping the enemy at bay. They will not be able to farm and if you do the job right they will have problems getting experience. Also, in case of a longer push you and your allies won't be running into any mana problems.
Teleport allows you to go back and forth for quick shopping or you can just use it for a quick kill/assist

I feel that I need some more help on this one, but the reason why I chose all CD is because you want to be able to spam bombs and rewind like there is no tomorrow

You want to get together with some other champ that is pretty good at harassing or a ranged champ to put some nice damage on the turret. Champions such as Teemo, Mundo, Kassadin are ideal. My favorite champion to lane with is Maokai. To be honest, I have not had a partner that was not able to dominate the lane with me. One champion that you do not want to lane against is Soraka, she will be able to heal faster than your damage output and while this alone will not allow her and her partner to leave the turret, you won't be killing or forcing them to go back to town. Even having them leave to town a few times during the laning phase will cause them to be under leveled, in other words they will be easy kills in team fights.
Team fights are heavily dependent on your team and how well it performs. If your tank is doing their job then quickly draw in to put 2 bombs at some squishy in the back and then retreat to a place behind your team (it is probably time to cast your ulti on someone right now anyway). If your team is struggling with the opponent's melee then just chill back and bomb the **** out of their melee. One thing that you want to do right before everybody is fully engaged is catch that one last melee and cast your time warp on them. This will give your team 4 extra seconds of less damage. It is crucial that you spam your rewind skill during team fights, you will be surprised to see that you will be able to cast a second chrono shift from time to time.
If some champ like Yi or Irelia decides to isolate you in team fights communicate this quickly to your teammates. Next fight just cast time warp as they are getting closer and let your team ruin their day. This will usually teach them from going after you.
Each composition of champions is unique so you must be able to tweak your moves, positioning and targeting each game.

You and your team will most likely be doing pretty well in the beginning due to Zil's ability to control the lane and the nice experience boost to all. This is why, you want to rush the deathcap as fast as possible so that you can continue doing damage with your bombs. The next item is Soulstealer. Even if you won't get a lot of kills, you are guaranteed to get mad assists and you will end up with 20 stack in most games. Ryalai is simple there so that your bombs and time warp slows down the enemies. Hourglass gives your team the time to react in case some melee decides to target you. Finally, we end it off with Lichbane just so you can really put massive amounts of damage on those squishies.
Disclaimer: This is an ideal build, given that you are skillful at using Zil and your team has an advantage (which they should). In case battles do not go as planned I would recommend to get Banshees instead of Soulstealer (especially if there is a lot of silencers on their team)