Can I transfer my OS (Win XP) and programs from old hard drive to a new one?

Today I bought a 500 GB hard drive for my desktop PC, which I plan on installing today. The current hard drive is absurdly small - only 50 GB - and I already have Windows XP on it, and a lot of other important software like Photoshop (CS 3 - all the later versions are trash to me), Steam, Alcohol 120 and various virtual drives, iTunes and a lot of music, and lots of other stuff that I DON’T WANT TO have to reinstall.

Is there a way to insert the new drive, and then somehow move the operating system and all of the programs and documents - in other words, my computer, as it is now set up - onto the new drive?

Yes.
Set the jumpers on the old drive as a secondary drive. Install the new drive as well. Use a free program to copy the old to the new without booting up the OS. I use a simple program on a floppy drive. You probably don’t have a floppy so you need a CD drive to boot from. Those programs are free too. Do a little Googling or listen here for programs people suggest.

EaseUs Todo backup seems to be the most recommended. It’s free, easy to use.

Can you install both hard drives into your PC at once? Or do you have a USB hard drive you can back up to?

You can transfer your O/S and files using a disk imaging program. Wikipedia has a list:

I’ve used Symantec Ghost and DriveImage (discontinued) with good results. Make sure your filesystem is in good shape (i.e. run chkdsk and make sure it completes with no errors) before making an image.

So…do I make a boot disk with that program (boot CD), then boot from that CD, after installing new HD as primary and old HD as secondary?

With the old drive still primary, install and run the software. When you start up the software, there are options to Backup, Restore, and Clone. If you can install both hard drives at the same time, Clone should do what you want. I’m pretty sure it will be able to copy the old drive, even though you’re running from it. After that, you should be able to just use the new drive as primary, with the old drive removed, and boot right up. Save the old drive unchanged for at least a while until you’re sure everything is working right.

There’s also a Tools tab, where you can make a recovery CD, DVD, or USB flash drive.

When I used it, it was on a laptop, and I had a USB hard drive, so I used Backup then booted from the recovery disk and did a Restore.

Oh, look! Disk Clone instructions.

ETA: Note that you can make the partition(s) on the new drive bigger, to use up the entire disk if you want.