A few basic suggestions:
1) Research and find a decent free host that offers website building for beginners.
2) Know the DSi browser capabilities and make sure everything works out on a DSi.
3) Learn HTML/XTHML, JavaScript, PHP--in that order. A nice place to start is w3schools.
4) From there, it's about whether or not you're willing to pay money for a reliable host that supports flexible coding.
And feel free to advertise on the Affiliate Website board. If your site has good content, consider applying for affiliation with DSiPaint.
I'd recommend you use either 000webhost, x10hosting or freehostingnoads as a free host if you're looking. FHNA and 000webhost are better than x10 in my opinion, having used all three.
It's my job to help the next generation, and set a good example for them. And for that I'll gladly lay down my life.