EVE New Citizens Q&A

The following skills affect torpedoes:

Torpedoes

Guided Missile Precision
Missile Bombardment
Missile Projection
Missile Launcher Operation
Rapid Launch
Target Navigation Prediction
Warhead Upgrades

T2 Torpedoes:
Torpedo Specialization

All weapons are organized this way (drones too). There is a primary skill that affects the weapon itself, several weapon support skills that improve range, rate of fire, damage, hit chance vs. smaller targets, etc., and then skills for unlocking the T2 versions of the weapon. The weapon support skills actually affect all weapons in that class, so the list for Heavy Missiles is the same, except replace the word "Torpedo" with the word "Heavy Missile."

Skills Explained.

EDIT:
In addition, if you're flying a bonused ship (the ship description says "5% bonus to Torpedo damage per level"), then the ship's skill also affects Torpedoes. So for example:

Caldari Battleship - trained to level 3 would give you 15% damage bonus, if you use Torpedo launchers with that particular ship that has the bonus. On top of the other bonuses from skills.

And then of course there are a number of modules and rigs that also affect missile damage, and torpedoes are missiles, so you use those on your ship to multiply the damage even further. Ballistics Control Systems, Target Painters, etc.

The heavy missile skill says "5% bonus to heavy missile damage per skill level." That seems somewhat cut and dry to me IF! you understand the various types of weapons.

Each weapon system will have a short range variant and a long range variant. They also will have different sizes: small, medium, large and extra large.

Small weapons are mostly for frigate and destroyer sized ships.

Medium are for cruiser and battlecruiser sized ships

Large are for Battleship sized ships

Extra large are for Capital sized ships

If you are ever confused on this look at the ship info under rig slots in the fitting tab and you will see: small, medium, large or extra large. The size rig that the ship takes is typically the size weapon it uses. A few years back CCP introduced a BC for each race that uses BS ( large ) turrets but aside from those I am aware of no other exceptions to this rule.

Also there are launchers for medium ships that shoot small ( light ) missiles but they shoot them fast and reload over a very long period of time and still have medium ship fitting requirements. Also you can put smaller weapons on a larger ship but the ship bonuses are size specific so those won't apply in that case.

Drones fly to their target so there are no long and short range drones just some that preform better under different situations.

For missiles:
-Light missiles are small long range and rockets are small short range.
-Heavy are medium long range and heavy assault are medium short range
-Cruise are large long range and Torpedos are large short range
-XL cruise and XL trops same thing for cap ships.

Projectiles:
-Artillery are long range.
-Autocannons are short range

Hybrids:
-Railguns are long range
-Blasters are short range

Lazers:
-Beams are long range
-Pulse are short range.

Missiles have a different skill for the short and long range version of each size. Turrets ( guns ) have one skill for the T1 version of both long and short range for each size and you only need separate skills for the specializations which are T2.

For example the skill "Small Projectile Turret" works for both small artillery as well as small autocannons. Same thing with the medium, large and extra large versions. Also same for small, medium, large and XL hybrids and lazers.

Another way that you can figure this out for yourself is to do a "show info" on the skill book and look at the "Required For" tab. There you will see highlighted the various levels of the skill that open access to something else. Click on the skill level in roman numerals at the top and see what it is required for. This should also be what that skill applies to. You can also go the other way by looking under the "requirements" tab on the show info of the weapon.

If this seems confusing don't worry you'll get the hang of it and after a while it will seem obvious to you. This game does seem much less confusing after a while so don't worry if you feel overwhelmed in the begining, we all did.

EvE HQ offers an answer to this problem. When you do a show info on an item it has a tab that lists everything that can affect that item, skills, hull bonuses etc. While I agree these should be available in game until they are this can help in a situation like this.
EvE HQ

I have not looked at them recently it is possible that EFT and PYFA offer this as well so you could look into them as well.
EvE Fitting Tool (EFT)
Python Fitting Assistant (PYFA)