I'm sure someone on here can give you better tips than I can, but I'll do my best to start. I have just recently tried this technique.
Basically distressing is grunging up your papers, embellies, etc. You can use a distressing tool to rough up the edges of your papers, ink the edges, crumple papers, rip paper instead of neatly cutting it, etc. The ones I have used the most is using the distress ink around the edges of the papers and the tool to rough up the edges. I just take an ink pad and run it along the paper or take a sponge or other applicator and use that to smear ink around and things like that. I don't think I have any examples in my gallery yet, but you can click on the items I have listed below and there should be things linked from the gallery that the item was used on.
Hope that helps somewhat. I'm sure I've only touched on the tip of the iceburg with it. If you have any questions, just let me know and I will try to answer them.
There are tons of different distress techniques. As the ladies in this thread already pointed out, sb.com is a great place to find vids and tutorials. I really like inking the edges of my papers, flowers, embellies. It gives them a burnt look without having to set anything on fire. Tim Holtz Distress Inks are a great tool because they are formulated specifically for distressing and they are reactive with water which can yield some fun results. I think you really just need to dive in and start playing around - have fun!!
I think inking is the best place to start with this - just grab a makeup sponge (or buy the Tim Holtz inking tool if you're so inclined) and a pad of Tim Holtz Distress Ink in Vintage Photo - I've found that it's by far the most versatile color to use, and boy to I use it on everything! Good luck!
I LOVE distressing. My number one tool is the Making Memories distressing tool...it has really saved my fingernails. I agree with papermouse- inking is the best place to start...and Tim Holtz does have really nice colours. Best of luck, you'll get the hang of it.