The sound of gunfire rings in your ears, you're outnumbered 3 to 1 and surrounded, but hidden. The odds are not good... for them. You draw your sniper rifle and screw on your very own silencer, pushing through bushes you aim at one guy with a fully automatic and fire, the whistling of the BB is heard and your target clutches their chest where they were shot. 1 down, two to go.

Before you start (this part is kind of long but I promise you that the rest won't take nearly as long)
Now, before you start please note that there are a few types of guns that cannot be silenced without extreme measures or internal modifications so shoot your gun and listen to it first.
Does it sound like an electronic noise (IE something hitting something else, the grinding of gears, or the running of a motor, ect)
if yes then your gun needs a full body silencer, I will not make a tutorial on how to make this without first doing more research on it so make sure than the noise from your gun is the noise of gasses escaping or popping of air release.

One more thing before we start, Do you have access to a tool shed or workshop? There are two types of silencer, one is the Ghetto Silencer which you'll find in most places, the other is a more professional silencer that can actually be used to silence real pistols. The other is much better so if you think you have the tools and materials you may want to follow the half of the instructions labeled "Professional"
(please note none of the pictures taken are of or from me, I just went Via google)

Step 1: All Your Cotton or Tennis Balls Are Belong to Me :P

Ghetto
You'll need some household materials, and your gun. One or two pop cans, a long sturdy tube of some sort(a stray is not recommended due to it being so flimsy), lots of cotton, and some scissors, possibly a kitchen knife. oh and tape, a full roll of tape

Professional
Two sizes of PVC Piping(one should be able to fit inside the other with room to spare and the smaller one should be able to wrap around the barrel of your airsoft gun), A sheet of flexible metal or another type of rigid material that can be used to cap off the end of the PVC piping, A drill with a smallish bit, about a billion tennis balls if you want to suppress the more powerful guns but some cotton or other fluffy sound absorbing material will do for weaker guns, a hot glue gun or other type of glue/material that will be able to connect your smaller PVC to your airsoft barrel, and finally a hacksaw(preferably a hacksaw, but I suppose another type of saw would work so long as it can cut your PVC).

Step 2: Let's Do This! ... That's What She Said...

Ghetto-
Start with the can/s, cut a hole in the side opposite of the hole that's already made(if you use two can you're going to want to make the holes in about the same place so it doesn't look funny), your rigid tube should be able to fit down these holes and come out the other end so it's all connected, but don't put the tube in yet(also what she said), first off, stuff your can/s with cotton till you can't fit anymore in there, or you run out, it shouldn't be super tight, about the density of a pillow only with a aluminum casing(the can), now poke a bunch of holes in thetube, not too big but not too small, about the size that a nail will go down. Put the tube down through and clear it of any cotton it may have picked up, now with the end of your tube that's sticking out, tape it over/onto the end of your airsoft barrel, and tada! it's done.

Professional
If you use tennis balls then cut off all the fuzzies on the outside of them and store the fuzzies in a cup or bucket. Use your hacksaw to cut the PVC down to size, the larger PVC should be about 2 inches shorter than the smaller PVC, the length of these should be fairly short but not too short, about 4/5 inches is good. Take the smaller PVC and put it inside the larger PVC, cap off the large PVC at one end, cut or drill a hole in the capping in the center large enough to fit the smaller PVC in it. Drill several holes going down the PVC about two inches apart each, put the now religious(holy, lol) PVC down the larger tube through the capping and through the hole, make some of the smaller PVC stick out about an inch or two, enough so the ends on the other side line up. Stuff the space in between the larger and the smaller PVC with your fluffy material, cap the other end and drill a hole in in the capping big enough so that all the smaller PVC pipe shows but none of your fluff. Finally Glue/tape/whatever the PVC sticking out onto the end of your airsoft gun and you're done at last.

Step 3: Fruit of the Loom, Hacksaw, Whatever...

Ghetto
not much work doesn't show for a whole lot, your gun won't sound of quite so loud now, but you can still hear it. Looks really ghetto but a very homemade touch to your gun.

Professional
Your valiant efforts have paid off, your eyes beam as you aim your new extension to your rifle and open fire, You grin a terrible grin as the thought rushes to your head, "they'll never hear me coming"

Um, buddy, it didn't work? This the case, then go on to the next step.

Step 4: Huoston, We Have a Problem

Problem 1:
Boom! plop.... the glint in your eye fades as the bullet lazily falls to the ground possibly doesn't even come out. This could be because your extention wasn't lined up quite right, if the bullet hits something before it exits the barrel it may just fall to the ground rather than shoot out.
Problem 2:
Bang bang bang! wtf? A feeling of lost time and confusion entwines with your thoughts, the silencer is attached properly, but it's still making noise? This could be for a variety of reasons, two of the most common are this, if it's muffled but still pretty loud, it could be because the holes you cut were either too big or too small, or this could also be that the material you used to stuff the cans/PVC was a low grade and didn't absorb enough sound.
Problem 3:
You lift your gun to aim and to your demise at even the slightest of movement everything comes undone and your silencer falls right off. You pick it up and glare at it and think of what you could've done wrong. The thing that may have gone wrong is one of two things, either your connection wasn't very strong or your silencer was too heavy, or a combination of the two. Try using stronger tape or glue to connect the silencer to your barrel, maybe shorten your silencer or even use less dense lighter material to stuff the cans/PVC.