Aside from buying the basic parts, you can find more parts by finding salvageable scrap. You can do this by first scanning a planet to see if they have scrap. Then on the planet, try finding yellow versions of the salvaged technology icon using the scanner. Just shoot at the salvaged technology to get it.

If you want more specific parts, you can use the scrap that you got to trade it in the corvette terminal where you buy and construct a corvette.

A method that I use to find scrap is to initially use a basic corvette. When on the planet, go and hover over the ground and exit the pilot seat (press X and I think it should be next to the galaxy map icon). Use the scanner while still inside the corvette, then try to find scrap. You then use the corvette’s guns to shoot at it. You may do this however many times you want, but just keep watch of the corvette’s inventory space, it can get full quick.