The first thing, of course, is to determine whether or not your wall is a bearing wall. Helpful tip: if you can't figure it out, don't start your work until you call somebody who can (your father-in-law is often a good bet, as are any architects or general contractors you might be hiding in your closets).
The basic premise of this whole process is that you've got to hold up your damn house. It's a pretty simple concept. So, if you're going to be taking out the wall that's currently holding it up, you'd better have something else in place before that support goes away. So, you build a temporary wall.
Don and his dad put the studs on their temporary wall 24 inches apart rather than the standard 12 inches apart because a) it's temporary and b) we all have big butts. Once it was built, we had an old-fashioned barnraising!
You'll notice that they installed the temporary wall about five feet away from the wall slated for removal, to give themselves space to work but also make sure that the weight of the house is still being distributed fairly evenly.
Once they had banged the temporary wall into place, making sure that it was square, they dropped a few duplex nails into it for security's sake (believe me, that thing is wedged in so tightly that it's not going anywhere). Finally, they installed diagonal crossbars for added support.
And at last, it was time for demolition of the old wall. As you can see, Don was quite pleased.