NOTE: I don't yet own any of these items, but I may buy one, I've just been reading about them recently so I'm just passing on what I found to you.
You need:
1) DS passcard or passkey
2) Flash cart
There's more options, like flashing your Ds firmware. Too tired to go into detail.
Good flashcarts are:
1) M3 - several flavors exist, using either CF, SD or MiniSD cards for storage
2) G6 Flash - excellent traditional cart with 512MB built-in
3) Supercard - uses SD or Mini-SD, not as good as M3 for GBA
4) EZ4 - uses Mini-SD
NEW flash carts coming this month for DS Lite (they don't stick out from the GBA slot) include:
1) EZ4 Lite
2) G6 Lite
3) M3 Lite
Here's a photo of the G6 Lite for example, looks like the Lite's GBA slot protector form the front. Pretty cool. Price is supposed to be around $40 - $60 or so.
http://www.maxconsole.net/?mode=news&feed=nds is a good place for more info