I collected some up to date info from a Thai language website.
To answer questions that you did not ask :
there is no more need to do a police report (as in the past).
Can go to the DLT office directly.
No tests to undergo.
New license card will have same expiry date as the lost one.
Thai International driving permit: can't be wrong to have it with you although it's not needed for the process.
Passport photos make no sense. Picture taken at DLT office as usual before printing new license card.
Of course you have to take your passport and do copies of main page, visa, permission to stay.
Two things I can't answer for sure:
New residence certificate needed? (TM30 OK? Can also vary by office)
Medical certificate necessary? I would get one, 100 to 200 Baht or so at any roadside clinic, valid for 30 days (DON'T go to fancy hospitals).
If documents complete it's done in a single visit.
Whether or not an appointment is needed/required depends on office.
(I could just walk in and as no tests etc needed this might work at most offices)