Zilean in laning

Support your AD carry by pestering your enemy AD and Supp with none stop bombs early on. You'll see early they do decent damage and keep your opponents on the defensive because they have massive range. When enemies push and over extend lane hit them with a Q(bomb) then slow them with your E so that your AD can do tons of damage, picking up early kills. Seriously Zilean's E is a super powered exhaust. Once you have his W(refresh) you'll be able to get off two bombs and an E all at the same time. Once you have your Ult R(super powered Guardian Angel) you and your AD can start to push lane significantly harder. Basically this is where Zilean shines, in lane. Sometimes you and your AD won't get a ton of kills but you will keep your opponents on the defensive causing them to get behind in levels gold and CS significantly.

Zileam everywhere else.

Once laning is over it's time for you and Zil to get insane amounts of life saves and assists. For starters I make sure to constantly use my W(refresh) outside of battle to keep my Ult's cooldown super short. Zilean's roll in team fights is huge. First off check who needs to be focus and hit them with your Slow(E) then follow up with a Q-W-Q Bomb-Refresh-Bomb. This allows you to deal damage to the focus target and splash any enemy champions near him, your E(slow) pretty much guarantees your team will get the kill, and you get to do all this safely out of range. You pretty much continue this process until team fights are over and won by your team because Zilean is just that awesome of a support. Also watch at all moments your Allies health. If low and they have no chance of escape then hit them with your Ult(R) and then attack your enemies with bombs and slows. Once your ally is revived hit them with your E causing them to get a huge speed boost and refresh and hit the enemy with you E causing them to slow. If ever you ally has some space between their attacker just hit the enemy with E to slow them that way you can save your Ult for when it is absolutely needed. Also, always, as you disengage from battle, hit your opponent with one last Bomb.