Something I've been wondering for a while. Street Magic gives rules for new spells. But nowhere have I seen game mechanics for new metamagic. How exactly does a character research them? Can a spirit teach a power as a metamagic technique?

Rules for creating your own metamagic techniques haven't been created, and it's really between the player and the GM. I suggest taking a look at the existing metamagics and spirit powers and follow a similar format when making your own.

As far as how metamagics are researched in Shadowrun, the methods depend on the tradition of the researcher but generally involve periods of experimentation (dangerous to say the least) and astral quests. See p.52 of Street Magic for possibilities.