Zilean's combo is simple. speed yourself up with your E (, or slow them down if they're running. Then land a Q (), shouldn't be hard. Then W () to reset cooldowns, Q them again, then in a few seconds your E should be back up, slow them down/speed yourself up, and Q-W-Q them again. If they're not dead at this point, just keep doing the same Q-W-Q combo, optionally E'ing yourself to catch up or them to slow them down.

After you've gotten Level 6 and a Mana Item, when your ult is down, spam W; it'll pretty much half the cooldown.
Also, use your ult whenever you think it might be necessary, cause even if you don't die, you can always execute yourself (While it's still on you) just to heal.
Best of luck, enjoy Zilean!

This is my first 4 games with this build: