Hello!

I am looking into trying something a little different this year with my artistic abilities this year and am considering trying my hands at tile set design for other people's games (with the first few being for free so I can build a portfolio).

Tho I am wondering what's the best approach to getting started with learning how to make tile sets. Any suggestions?

You could try LibreSprite's tiled mode, which I believe* allows you to create tiled patterns easily.

*I haven't used LibreSprite myself, but I believe it should be similar to Aseprite's tiled mode, since it is a FOSS fork of Aseprite.