The handle is held in place by a combination of good fit, a strong epoxy, and for maximum strength, pins. Now it is true, especially with hidden tang construction, that you do not need pins (epoxy does the job just fine), but the increased security and strength is incredible, and plus, it really adds to the look.
The pin material doesn't matter all that much, as it's in a small enough area where brittleness or softness won't be a big deal. My first few knives even used wood, which isn't a bad option. Brass, nickel, steel, copper, whatever. For pins, really the material depends on the right color combo. Usually, just match the guard material or color. Design, fashion. The fun stuff. For a standard, I enjoy something like brass or copper for the vibrant red/brown toned materials (especially if it has a lot of character; spalting, burls, etc.), silver colored for the black or whitish materials, or those that have little character.
The diameter of the pin is once again mostly hinging on design. Slim, flowing knife? Thin pin. Bulkier camp knife? A little thicker could be appropriate. Full tangs also can merit a little thicker of pins. Usually if there are quite a lot of pins, I'll keep them on the thin side. In general, I hover around 1/8" thick. A standard size makes it easier to always get a good fit, and the lack of size variance generally doesn't matter all that much, especially as I can peen them over to make them appear thicker.
Drilling Holes for the Pins
With full tang knives, I like to drill the holes in the correct places in the tang first, then place the tang on top of a scale, drill one hole all the way through both the tang and the wood, insert a temporary pin, then drill the rest. From there, I'll do the same to the other scale, fit it all up with temporary pins, then shape the handle. If I intend to peen, I then remove and replace with slightly longer pins.
For stick (hidden) tang knives, I make sure all the pieces are as tight together as possible, and carefully drill through the wood in the spot I want. I usually only do one or two pins for a hidden tang. When the drill hits the tang, I let it press in a bit, then take it apart. I find it more reliable and a lot straighter to then find the mark left by the drill bit in the tang, and drill through that spot separately. This keeps it where I can see the progress, and oil or tweak if need be. Once I'm through the tang, I'll reassemble and finish drilling through the wood.
Note: peening takes a few tries to get right, and requires a lot of control and precision to do. My advice is to practice on scrap wood first. A mis-strike can ruin the entire handle, and at the very least merit re-shaping
Peening is the act of mushrooming over the top of the pin with a hammer, turning it into sort of the head of a nail. This makes the pin a permanent rivet. Proper fitting and peening can eliminate the need for epoxy completely, but I always use epoxy anyway. For starters, peened pins should only be put in once the handle's been otherwise fully finished; you can't do any further shaping or sanding with it in.
First off, make sure the pin material fits the hole tightly; any wiggle could result in the pin crumpling down on itself.
When you cut the pin material, give about an eighth of an inch (or less, depending how steep of a dome or how wide a mushroom you want) protruding on either side, maximum. Sand the tops flat and smooth.
For the peening itself, it's important to remember to give light taps, take it easy, make sure you're precise, and go slow. Use a ball peen hammer with a smooth (many people even polish it) ball and face, as well as an anvil with a smooth face. The lighter the hammer, the easier and more precise.
Balance the knife on its side with one end of the pin on the anvil. The pin should be vertical and the bottom end should be the only point of contact on the anvil. Think of the knife as only being there to hold the pin straight. If the handle itself is place on the anvil, you run the risk of damaging the wood.
Start with the ball side of the hammer, lightly tap, using mostly the weight of the hammer. Tap in the center, then vary around the top. The indents will mushroom out the top of the pin. Do more of this if you want the top of the pin wider and flatter, less if you want it thinner and more domed.
As you peen, flip over back and forth and try to keep either end of the pin the same. You don't want to do too much peening on one side, as you'll use up your extra pin length and have not enough to make the other side equal. Asymmetry is one of the signs of a poorly crafted knife.
Once you've mushroomed out a good bit (I usually do this until I've got enough space underneath the lip of the head to barely fit a fingernail), flip over the hammer and use the flat face. Light taps, eliminating the indents on the top, then start varying all over, doming the pin. Eliminate any facets, and try to get a perfect dome. Be careful here, a mis-strike means hitting the wood, denting it, and meaning you'll have to carefully drill out the pin, remove it, re-sand the wood, and try again.
Make sure the pin is tight on the wood, with no gap between the lip of the head and the wood. It should be perfectly circular, and smooth with no facets. Once again, it's tough to do on the first try, so practice is a lot of help. Once you're confident you've got it solidly peened, run over it with fine grit sandpaper to get it smooth (possibly unnecessary if you used a polished anvil and hammer). Clean up, polish if you like, and you're done.