Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
I made this build for someone who isn't pro, its pretty simple to execute as long as you are careful, and late game the enemy will be cursing your name.
Get the archangel staff as quickly as possible in order to maximize your mana gain from spell use, as well as making sure you always have mana, I very rarely run out of mana after i get the staff. To make up for he lack of speed you should just keep your distance for now, you will be slow for a while, but if you play it safe and stick by your tower its unlikely they will kill you. Make sure you use your bombs and rewind to farm, after you get enough AP you should be able to kill both the fighters and the wizards if you time it right. (i generally put a bomb on he fighters, then a bomb on the wizards, and then try to hit the fighters with my physical, if you hit each of them once or twice you should get the kills when the bomb explodes.) To harass, just try to stick a bomb on your enemy when you get the chance, and if they get cocky and go near you with less than half life, double bomb them and ignite them, but be sure to never over reach, especially before you get your boots, a death costs a lot for your farming.
After you have your boots and are likely past level 6, you can start killing some people, farming is still very important at this stage, cause a good Zilean can kill an entire wave, which is about 100gp per wave. If you are trying to solo, stay close to your turret if possible, withing flash/time warp distance. First double bomb, then put on chrono shift and then ignite/hit them, if hey start to run time warp them, and just try to get as many bombs on them as possible. Thats why rewind is so important early, it will keep your bombs going, as well as let you get rid of your cooldown on chrono shift, if you aren't fighting i suggest spamming rewind, it costs very little, comes back very fast, and will reduce the cooldown on chrono shift, as well as build up your archangels staff.
If you are in a group, just hang in back if possible, put bombs on people, and slow them down when they try to run, and make sure you watch your allies life, if you can prevent one of them from dieing there is a good chance you will get the kill from the fight they were in and you will make sure the enemy doesn't get the kill. (also your allies will love you for it)
If by this time you have not won your last two items should be more dedicated to countering your enemy, I usually do void staff and deathfire grasp, because it is effective against tanks. You will wanna hit them with the deathfire staff, then double bomb them, and maybe ignite, with the AP you have you should be able to kill them or at least hurt them badly, also with your massive cooldown you can probably get off at least 3 or 4 bombs and 1 or 2 time warps before the get away from you. Make sure you support your team a lot at this stage, because if you have late game team mates most of them will be much more effective than you in some ways, so giving them two lives makes them twice as effective. I generally timewarp my friends before myself because unless i have a bomb ready its a lot less likely for me to get the kill, but your ally may have a stun which will give you a chance to catch up and slow them and bomb them to death. Zilean is an effective assassin, but he is also amazing support, if you get greedy he can die easily, but if you are a team player he be an amazing addition to any team.
Archangels staff - this item is key, it has 25/5 mana regen and gives a substantial amount of ap and mana, it grows as you use it which makes getting i early ideal, especially for Zilean, because all you are usually doing is using spell after spell, 3 or 4 at a time. Once you have it you will likely never tun out of mana again, and it will likely put you at around 100 ap or more, which makes for amazing early game farming. I strongly suggest getting this item first.
Sorcerers shoes - This item explains itself, it will make you faster and deal with a small amount of magic resistance. I suppose if you really wanted to be able to chase someone down you could get faster shoes, but I personally wouldnt want to give up the penetration.
Glacial Shroud - I recomend this item in particular because 1, it adds mana, which raises your ap, and at the same time reduces cool down so it increases your potential damage and ability use, also it adds some armor which is great against early physical players and it has growth potential if the game drags on for a while.
Zhonyas Ring - needless to say this item is just disgustingly powerful, and once you get it you should be well into the 300's of AP.
Void Staff - this is where things begin to be very interchangeable, you can easily mix and match the void staff and the deathfire grasp, it really depends on what your fighting. If they have ALOT of hp you probably want to switch your order, but i do voidstaff first because it significantly increases my potential damage against the magic resistant.
Deathfire Grasp - When your enemy has 3k or 4k hp the deathfire grasp will sort them right out, a 30% 1 hit and then two or three bombs on top of them in sure to hurt anyone Its devastatingly powerful and completely interchangeable with the void staff. Also the cooldown isn't bad either.
Frozen Heart - This is what I buy when I have nothing else to spend my money on, Its a pretty decent item too, sometimes i get it early if my enemy relies on speed to do his damage, because the armour counteracts the low attack damage and the speed reduction is just awesome. All in all this is just a nice item to have around.
Banshees Veil - I pick up one of these in place of the glacial shroud when i am faced with a few casters, or another Zilean. Against Zilean this item is just painful because it kills your first bomb, which is about half of your damage. If you ever see someone with one of these on, i recommend that you use your speed debuf on them first and then put your bombs on them so they actually go through. The life and mana are also nice too, and its not very difficult to adjust for the loss of cooldown reduction.
Mejai's Soulstealer - Generally I never use this item because it depends far too much on not dieing and also being able to have a lot of access to kills. I have seen many people pull it off, and if you think you can then you should do it. Again i would replace this with the glacial shroud, but only if the other team was really gankable. I generally never use this item, but that doesn't mean its a bad option for someone who can pull it off.