How do I get Tali's companion quest?

The wiki tells you all (but beware of spoilers). Tali's quest is much more subtle than that for Garrus and Wrex. On Virmire or Feros, you can find information about Geth incursions in the Armstrong Nebula (as a side note, I can't say I've ever found the info on Feros, but that could be because of my low decryption skill for most of my playthroughs). As is typical, simply traveling to the Armstrong Nebula will prompt Admiral Hackett to tell you about it as well. It's during this mission that you'll find important information on the Geth that could be useful to the Migrant Fleet, and would do well to serve as a Pilgrimage Gift. Talk to Tali after completing Geth Incursions to also complete her side quest.