How might I print onto 3×3 sticky notes?

Printable post it - found on e-bay. Tested. It works :) Smaller ones are also useful!

You can get A4 sized printable label sheets. Those you can print on using any standard printer. Just feed this special sheet into the tray.

You need to download a word table template with the right spacing & cell sizes.

Avery is a popular brand. Don't know the official name but I always thought of those as printable label sheets.

e.g. see here

Since I have had glue from sticky notes and envelopes melt in my laser printer before, I would advise a different approach. (This is also helps with the fact that most larger laser printers I have seen won't print on anything smaller than 8.5 x 5.5 inches (half letter, approx A5 european size).

Print whatever it is you want to print, cut it out, and apply Removable Restickable Glue to one edge of the back of each cut piece. (That link is to 3M "Scotch" brand, but there are several other brands and you can find it at most office supply stores.)

This has an added benefit that you can vary the size and even the shape of the notes that you have if you desire to do that.