How can I extend my 30-day tourist visa in Thailand, and when should I visit immigration for the extension?

There is no 30 day tourist visa 🙁 if you showed up here without having bought a visa from a thai consulate before you got here and were stamped in FREE for 30 days you didn't get in on a tourist visa, or a visa on arrival, it's not a visa at all just a free entry stamp called a Visa Exempt Entry.

Most offices will let you apply for a 30 day extension on that visa exempt entry stamp when you have 30 days or less left on your current stamp.

Some offices make you wait until you have 2 weeks or less (and some say when you have one week or less).

Seeing as you didn't mention where in thailand you are and that there are OVER 80 offices you will have to check with your office to see what their policy is

You don't lose any days going early because the add the 30 day extension to your current stamp's expiration date.

this is a rough idea of what you need to apply for that 30 day extension at most offices