I would like to know how to record speedruns on ds and other hand held consolses.

you can just record your self playing it with a phone camera or something, also welcome to the site!

Like Tutterey said, pointing a camera at the screen is the basic way to start. You could try to set up a tripod with a phone camera. A more expensive but more comfortable option is to get a capture card. Good maker, but not in stock this moment: 3dscapture.com

Depending on the game, you could also download it on Wii U Virtual Console.

DelfinoCustoms has some hardware in stock, which is where a lot of the Pokemon runners have gotten their stuff recently. Not exactly cheap, but good reputation. https://delfinocustoms.com/shop/

Also keep in mind this doesn't come with a capture card. A good capture card will run you like $200 USD, although you can find some lucky deals on Ebay. I got my HD60 Pro on Ebay for like $150 CAD

Recommend following https://twitter.com/CountCreep and https://twitter.com/delfinocustoms on Twitter

@Meta What do you mean it doesn’t come with a capture card? Is that not what that website is selling?

Nope. DS's don't come with any HDMI output which means you can't natively hook up a capture card to it. The site is selling modded DS's that do have the HDMI out so that you can hook up a capture card to it

I’m confused. That site clearly advertises that they’re selling 3DSes with capture cards installed. I don’t see a listing for an HDMI mod.

Oh yeah looks like you're right, my bad. Looks like you just connect it to your PC and record it with OBS or something, neat