Alright guys. This is my first build. I made this build to get away from the Rod of Ages builds I've been seeing. I'm not really a fan of RoA, costs so much gold. So this is what I think Ziggs should look like.

So I chose these runes to maximize his early game potential, with lots of AP and mana regen. Ziggs should be able to harass the enemy with his bomb as much as possible. The range is outrageous and the cooldown is fairly low, oh, and it does tons of damage. Once you get good at throwing bombs accurately, you cannot be stopped.
So mana regeneration runes will give you more sustain.
Ability Power gives you more damage obviously.
You can use Magic Resist to reduce your damage taken from the enemy mid. I prefer the Ability Power though, its a lot more fun.

I chose exhaust because of the potential to keep the enemy from running away. Once your hexplosive minefield is used, and you are near the enemy, pop the exhaust and keep throwing bombs. It will help if they are attacking you also. Reduces damage greatly.

Flash is a standard in my opinion. Sure you can use Satchel Charge to escape, but that's every 20 seconds. Better have another method of escape.

Sometimes I will also used Teleport and Flash. Teleport allows for a constant farm, so you can just Recall, then Teleport back. It is also great for ganks, as you can teleport to an ally ward. And of course if you need to cover a turret in case of emergency. Many uses for Teleport.

Ignite is also a favorite among Ziggs users. Just gets that extra damage over time to get you the kill. I like it and all, but you need to be fairly close, and I'm not a fan of getting up close and personal with another champion, it leaves you vulnerable to stuns and other bad things that put your life in jeopardy.

Clarity is also a good summoner spell as it will grant mana to Ziggs. Ziggs burns through mana fast because of his ability to constantly throw bombs at the enemy champion. Definitely good for sustain.

I never use Heal. I guess its good for sustain or in emergencies, but I think it's easy for Ziggs to escape.

So I rush Needlessly Large Rod... Why, you might ask? Well it gives a nice damage output, and also allows you to farm mage minions with one bomb throw. Always good to have that at your fingertips for a faster farm. Also, it deals great damage to the enemy champion, which is always important.
Sheen is a MUST! Your AP gets so high, that when it combines with your passive, you deal over 1000 attack damage. Perfect for demolishing towers or champions, whichever you prefer. Lichbane eventually, just gives you more Ability Power and Magic Resistance.
Obviously get Will of the Ancients for its bonus AP aura + spell vamp aura. Can't go wrong with that.

So basically your goal is to put so much damage on the enemy team that they literally just melt. Try to get the enemies concentrated into one area, so that you can use your ultimate and ruin their days. This works really well with an Amumu ultimate, or another AoE stun/slow like Nunu's ultimate.
Oh, and the great thing about Satchel Charge for team fights... You can either escape with it, OR you can disrupt a channeling skill... For example, when Karthus uses his ultimate, throw it on him and detonate, this will interrupt it, potentially saving your team. Unless of course Karthus is dead and using it in his passive. Another example would be Nunu's ultimate.

I start with Bouncing Bomb first because it allows for harassing of the enemy champion. Definitely max Bouncing Bomb first for maximum damage output.
Hexplosive Minefield is definitely second, as it slows the enemy champion, and deals great amounts of damage. It was nerfed, but not to a great extend to make it non-lethal.
Satchel Charge is great for escaping or knocking the enemy out of place, but get this at level 3 or 4. You can use this to launch yourself over walls for perfect escaping, or to knock the enemy back if they are escaping from you.
Mega Inferno Bomb (Ultimate) is such an awesome ultimate. Massive damage in the center of it, 75% damage around the center. What a great way to deal A LOT of damage.
Basically just keep throwing Bouncing Bomb at the enemy, then when you think you can finish them, move in somewhat close, throw Hexplosive Minefield behind then, or in their escape direction. Once they are slowed, keep hitting them with Bouncing Bomb. When the slow is done, pop exhaust if needed, or throw a satchel charge in front of them, detonate so they are pushed backwards. Don't forget to hit them with your basic attack, as your passive will enhance your damage greatly. If you need to finish them off, use Mega Inferno Bomb to mess their day up.
Another method I like to use is to throw down Hexplosive Minefield, wait til they are slowed, they throw down my Mega Inferno Bomb. The slow will keep them from escaping the center of the bomb.
Once you get the hang of Ziggs, you WILL be a powerhouse. Just be smart with your moves.