Have I convinced you not to do it yet? No? Sigh. Ok then, don't say I didn't warn you.
The Important Bits
A bomb travels in a straight path for 30km then explodes, the explosion affects an area 30km in diameter (or 15km in radius).
This is extremely important to remember. Let's say your ship is sitting still and not being exploded, the explosion from the bomb you just launched will explode 30km from your ship, but the radius means the damage from that explosion will only reach 15km from your ship - cause the rest is on the other side of center in a 360 degree sphere 'o doom. Got it?
Next. You don't target anything to fire a bomb. It is a line-of-sight weapon, so you simply point your ship at your target and launch. The bomb will travel straight out from your direction of travel for 30km (or aprox 10 seconds) and then explode. Once launched a bomb always explodes, there is no stopping it unless... but that's later down the article.
Now here is the critical bit about launching. If you launch and then immediately warp away, your bomb will fly off in a random direction and won't hit nothing. This represents the enemies opportunity to target you and kill you, which they will often succeed in doing. (Hence the exploding you will be doing!) Once fired you need to wait, I usually count out 1,001, 1,002, then hit the warp button. This ensures a straight path for the bomb and usually time enough for the enemy to lock and kill me. Got it?
Now things get even more complicated
It's important that you not die doing this. No matter how much of an Idiot you happen to be, I would think you would agree. So let's work on ways to make you more likely to survive.
Line of sight is very important when bombing. Not only does it provide for the bomb path, it also provides for your escape. To survive a bombing run you need to prepare ahead of time. Let us take bombing a Gate for example. Since this is probably the most popular form of bombing, it is a good example.
Prepare a Bomb Spot. A good Bomb Spot is 35km from the target Gate in-line to a celestial. In other words, you should be able to draw an imaginary straight line from your spot, thru the Gate and straight thru to a distant celestial object - like a planet, moon, something like that. Even safe spots work now that you can align to bookmarks, but that can be tricky. Also, I wouldn't recommend Asteroid Fields, they tend to de-cloak you when you land. (Something I discovered the hard way once!)
Why 35km and not 30? This becomes personal preference, but I prefer a short path to gather my thoughts and prepare mentally right before I suicide... I mean launch the bomb at the enemy gate camp. 5k is a nice buffer to do that, my ship gets up to speed and my fingers hover over the appropriate buttons while I mentally try to remember all the things I need to do and do very very quickly. Those things are, in order:
-1: I am cloaked in a bomb launching stealth bomber 35km from the target Gate.
0: I am reasonably sure I really want to do this.
1: I hit approach to the target, by double clicking in space or hitting approach to the gate.
1b: I select the warp-to Celestial I am planning to warp-to if I live long enough to do so.
2: At the 30k mark I de-cloak, launch the bomb and start counting 1,001... 1,002...
3: I hit warp-to the celestial I had previously selected. Because my ship is already aligned, my ship will almost instantly warp away.
4: Sadly, bombers never get to see the bomb explode, but hopefully your screen is full of damage notifications. Be sure to check your combat sheet to see if that bomb kilt anyone.
More about bombs
As with all things Eve, it isn't even that simple. Oh no, it gets more complicated.
Damage. All bombs have a damage type, just like all other ammo, kinetic, thermal, etc., there are even special types of bombs. But this guide is about bombing, not bombs. The important thing for you to know however, is that different damage types cancel out the other types. This is weird, so pay attention. Let's say you fire a Kinetic Bomb and your idiot cousin fires a Thermal bomb at the same approximate time at the same approximate target. Sadly, whichever bomb explodes first will kill the other bomb. However, if you both happen to fire the same type, they will both explode. In other words, Kinetic bombs are invincible to Kinetic damage. And the same holds true for all damage types. Make sense?
This is why fleets of stealth bombers are always grouped by damage type. Kinetic Wing, Thermal Wing, etc. Cool huh?
How do bombs damage ships? It is an extremely complicated mathematical formula which is impossible to understand, but in simple idiot terms it works out like this: Signature Radius of the target, distance from center of explosion, resist against damage type = amount of damage sustained. This is why you never ever engage your microwarp drive when a bomb is headed towards you! Don't do that. Or in this case, hope the enemy does it. Frigates, interceptors, and other small ships might insta-pop with just one bomb. Bigger ships will sustain damage. Bombs are also very effective in killing drones, if they happen to be in space at the time.
There is more to it. But those are the basics, the rest comes down to practice, experience and dozens of horrible deaths.
Enjoy!