These are brief lowdowns on the various weapons Edward uses. Since we're given the names of the types of guns he uses, but not specific models, only so much can be given about those.

Holy water
An obvious weapon against vampires, holy water is simply water that has been blessed by a priest. Sometimes Anita carries a bottle of it (or she has it in her vampire kit). Holy water is like acid to vampires; it can severely burn them. Valentine was a vampire that Anita used holy water on; he got a permanent scar on his face from it.

Edward and Anita also use holy water to cleanse vampire bites. If a vampire bites you, it can gain control of you, so the bite must be cleansed. Cleansing with holy water is torture; it's extremely painful. Afterwards, a cross must be pressed up the wound. If nothing happens, you're clean. If it burns you, you are still tainted.

Silver nitrate
In Guilty Pleasures, Edward and Anita raid some coffins, and Edward shows Anita a disturbing method of killing vampires; he inserts needles filled with silver nitrate into the veins. Silver nitrate is a notable silver compound and is considered a pure metal. It is popular in many cultures as a form of protection; objects made from silver are often used to ward off evil spirits and such. All this explains why the silver nitrate could harm vampires; it is like poison to them. Silver also gives vampires wounds which cannot heal.

Garrote
A garrote is a strangulation weapon. There are different forms of it, from thin wires to collars and such. Edward carries a garrote in Obsidian Butterfly. It's a thin wire that he hides in the brim of his hat. Anita points it out when she is temporarily capable of vampiric sight.

Flamethrower
Anita makes a reference to Edward even before he is introduced into the series. She talks to Philip about how she once saw a man use a flamethrower on vampires. In the next chapter, it is noted that Edward was that man. Edward doesn't use a flamethrower again until Circus of the Damned.

Whether you're a vampire or a human or a lycanthrope, having a stream of fire projected at you is not a good thing. A flamethrower is a hand held fire projector. It basically launches liquid fuel that gets ignited. The modernized flamethrower consists of a small gas tank that holds the fuel and a pressure regulator. This tank is worn on the bank and is connected to a hose/pipe, which is connected to the ignition (the gun part).

Darts
Edward has these in Obsidian Butterfly. They're very thin and tiny, and he wears them in a band that goes around his chest, with a pocket in the front to hold the darts. There's no particular reason why he has these; Edward just likes to pack up as much arsenal as he possibly can. However, he has excellent accurancy when he throws these darts.

Beretta
This is Edward's main weapon; the one one AB fans identify him with. The Beretta is an infantry small arms weapon noted for high accurancy, lightness, and rate of fire. Beretta models tend to be lighter, smaller, and more lethal than regular guns.

Sniper rifle
Edward brings along one of these in The Killing Dance when Anita has to go to the Lunaper. It's a pretty serious thing when Edward comes bringing a sniper rifle; it's obvious he worries for Anita's safety, and he is certain someone will go and try to kill her. Edward and his backup, Harvey, position themselves at the top of a hill while Anita heads for the Lunapar. The modern sniper rifle is a scoped rifle used to shoot targets at long-range.

Bullets
Anita points out in that Edward does something neat with his bullets. He takes hollow silver bullets, fills them up with mercury and holy water, and then seals the ends with wax. The result is a shot into a vampire that ends up exploding, burning and eating at the body like acid.