Zeus is the first Dota hero I became comfortable with. It's the first one I had a real fun with, as I didn't spent half of my game watching at the respawn timer (when I was at my first games, my Crystal Maiden was the best source of gold income for the enemy team). Zeus is a really nice ganker, and it's one of the few casters that can still output some decent damage against the enemy team during late game. More than anything, you can annoy the hell outta your foes thanks to your ultimate. Don't forget that making the enemy rage is the key to victory in Dota: if one loses his mind, he will lose the game too.
Awesome voice responses
No real disable
Your skills are what you will be relying on when playing Zeus. Your right click is quite bad, so don't expect an easy life early on. In fact, the 2 builds I posted are not good for laning mid against a right-click damage dealer like drow or sniper, as they will prevent you from getting any gold early on. But if you face those heroes at level 7, you can be pretty much sure they don't stand a chance, 1 on 1. Sure, they are gonna hurt you. But you are gonna hurt them much more.
Your Lightning Bolt is your best friend. It deals damage, has a 6 second CD, and gives you true vision around the area. I cannot stress how much important this is, especially early in the game when you are facing a Templar Assassin, Bounty Hunter or clinkz, and riki once he gets 6. When the enemy has those heroes, make sure to have always enough mana to spam your lightning, buy more clarities or mana regen if needed.
Zeus is a decent counter against stealth agility heroes, mostly because they have little HP and you can scout them easily. I can't count how many times I was quietly farming in my mid lane, threw in a thunder just to make sure Riki wasn't right beyond me, and find out he was. Trust me, this practice can save your and your allies life. It's also a nice skill to ruin TA early game, since she won't be able to juke and meld when low on HP. Last but not least, remember that dust + zeus = no place for stealths to hide. One last use is on bottom or top lane, when the enemy tries to hide in the threes take one enemy creep close to the jungle and light it. Here, you just spotted your running foe.
Arc Lightning ain't a bad skill, too. Make sure to have at least one point in it before the big teamfights begin. You will be spamming it once every 2 seconds in order to maximize your passive damage. It's also a good skill to burn the enemy clarities or salve/tranquil boots, so you might want to take it at lvl 1. In one of my builds I take it quite late. The rationale behind going pure nuke is quite simple: with 2 levels of static field and 4 levels of lightning, you are able to deal 350 + 350 + something around 10% of an enemy HP in 7 seconds at level 7, plus your eventual ultimate if you have mana for it. That's a heck lot of punishment, and if you do cooperate with your allies you WILL be scoring assists. However this build might not be the best, it really depends on the enemy lineup.
Your ultimate has more than one purpose. First idea is: use it to secure a kill. This does not only mean "HEY! That Queen of Pain blinked out with 10 HP! Zeus, ULT!". Suppose you are ganking with a stunner like sven and you find the enemy Nature's Prophet in his jungle. He sprouts itself so he can start teleporting away. It's ultimate time! You will get vision of him, then proceed with Lightning to cancel his TP and keep good vision of the area. If your ally is not brain dead, you are gonna score that kill.
Another good use is during team clashes: your ulti deals some good "AOE" damage, so it can be a good idea to use it at the beginning of a fight to soften enemy heroes.
One last note: when facing Templar Assassin, remember that you are one of the few nukers that can really help to take her down. Every time you hit her with a spell, she takes the damage 2 times: one for the skill, one for the passive. With one combo during a teamfight (arc, ulti, light, arc), you have eaten her shield and left her naked in 2 seconds time even if you didn't target her directly.
The 2 item builds differs a bit depending on what role you want to have in your team. If you want to go for pure nuking power, I highly suggest you to go for urn. This gives you some decent strength boost, mana regen and nice HP regen provided you are able to actually kill your targets, all for a dirty cheap item that comes into small parts.
Some HP boost is mandatory on zeus: you really cannot afford dying more then a couple of times early on, because it will ruin your gold income and experience, making you less effective really quickly. Some people get escape items, but I suggest you to go for tankiness and stick to your allies, so that your friends will have time to react and save you (or take revenge for your death). I just love bloodstone; it's invaluable for high mana regen and keeping up your experience gain (you may easily die at the beginning of a teamfight) and since you already have arcane boots, you can disassemble them and have your soul booster come with only 2300 gold. This means you can get a decent mana/HP regen and 450 bonus HP quite early. I usually go like: boots of speed, urn, arcane, vitality booster, point booster -> soul booster, new pair of boots (I like threads, but go whatever you want) then complete bloodstone.
In one match I had luck during early game and scored a lots of assists/kills without dying once. By mid-late game I had a bloodstone and other HP-boosting luxuries. With 2400 HP I was the tankiest hero on my team. Spirit breaker charged me under my T2 tower and the whole enemy team came after a few seconds, looking for an easy kill. Sure, they managed to get me, but it took them so long that my team came for payback, and they got teamwiped :P
I suggest you to never go Aghanim as first big item unless your team is really leading the match, mostly because you are a bit squishy at the beginning. IMO is better to get Aghanim as second big item. For example, a hood of defiance might save your life if the enemy magic damage is huge (pudge, lina, lion). Even a BKB will be a better item then Aghanim if the enemy team has too many silencers/stunners.
When facing strong right-click heroes, some situational items are recommended. If the enemy has an agility carry, chances are that a blademail + your nukes will be enough to keep them at a bay, and maybe even score a counter kill (it's sweet when a Phantom Assassin comes at you without a BKB and you pop your blademail, then W and R: she's dead before she can stop autoattacking). If you are facing strength heroes or BKBers, a ghost scepter might be a better idea instead. If they have slows or they pick a Nature's Prophet go for that force staff, and farm it FAST. Your don't want to rely on tangos for saving yourself or teammates :D
Zeus is a nice intelligence Hero. It's really funny to play and has more tricks up to his sleeves then one might think. It has it's own share of counterpicks, but if you get the right items quickly and stick to your team you won't have anything to fear. Just remember to play it safe: you are no longer immortal, so don't ever try to initiate team clashes or chase blindly one (apparently) lone hero. Keep an eye around for any good use of your ultimate, work with your team and you will enjoy your time as a God.