Tools you need
The great thing about collage is that you need only a few tools. With just scissors, glue, and paper you can remake the whole world. However, if you want more particulars, read on:
Scissors:
A good pair of scissors should have a sharp blade, a comfortable grip, and a sharply tapered tip. If you have a chance, test the cutting action before buying--the scissors should open easily and close smoothly, without a jerky motion. A sticky pair of scissors makes it difficult and time-consuming to cut out small shapes smoothly. I haven't found the perfect pair of scissors, but I use a classic 8-inch pair of scissors from the office-supply store and they work just fine.
Razor blade:
Although it's not completely necessary, a razor blade or X-Acto knife is often useful for precision cutting of tight corners and cutting out interior areas, such as the inside of a teacup handle or the space between an arm and body.
Glue:
If you're starting out in collage, I recommend using a glue stick rather than white glue in bottles (like Elmer's glue). I use glue sticks for most of my projects. They're a little more expensive than plain Elmer's glue, but they're much easier to use, because the thicker paste can be applied evenly to the collage cutouts. The downside of glue sticks and white glue (at least the ones from the office-supply store) is they're non-archival, which means your art might begin to deteriorate in 50 years. Archival glues and glue sticks are available, but they tend to be pricy.
Weights
Collage is working with paper. It's easy for a small breeze or just the motion of your hand to move the paper, changing your carefully crafted composition. Use small weights to hold down your work as you craft it. I've got a little block of marble (it's from a disassembled bowling trophy), but a large coin, a paperweight, or any other small flat object will work.
The basic tools: scissors, razor blades, glue (a glue stick and liquid glue) and a marble weight.
Work area:
Clear yourself a horizontal surface to work on. You'll need an area to arrange your collage and a nearby area where you can apply glue. My work table is covered with a sheet of glass, which makes a nice backing for delicate razor blade work, and is easy to clean. You don't need glass, but you do need a surface that is either easy to clean or disposable. If you use a razor blade, you'll also need a backing surface. Again, glass is nice, but a heavy cardboard (like the back of a paper pad) will also work.
My work area, covered with collage material.
Scrap paper:
You'll need some scrap paper that can be disposed of to do your gluing on. You need enough so that all your gluing can be done on a fresh piece of scrap: you don't want excess glue that's supposed to be on the back of your images to get stuck to the front, so use and discard your scrap paper frequently. I use the excess scrap paper from cutting up catalogs, but a newspaper will work fine.
Tips
A good pair of scissors
The most important tool is a sharp pair of scissors. It can take twice as long to cut out images if you're using a dull pair.
Rubber cement
Three words: Don't use it! Rubber cement will brown your paper as it soaks through. It seems like an easy solution to a sticky problem, but if you use it, you'll wish you hadn't.
Applying liquid glue
I usually use a glue stick, but when I use liquid glue, I apply it with a small paintbrush. The paintbrush applies the glue in a uniform coating, preventing pools of glue from wrinkling the paper.
Using a new product
If you're using a new product--glue or clear protective spray or whatever--test it on some scrap pieces first. Some products will discolor an image, and if it does, it's better to find out on a disposable test scrap than on the centerpiece of your newest collage.
Save that phone book
I don't use this method personally, but other collage artists suggest using an old phone book as scrap paper. You can flip to a new page each time you apply glue.
