How do I apply for a re-entry visa at Suvarnabhumi Airport, and what is the process involved?

They do all the work for you as well, 1200 baht for a single entry, cash only. located between security and immigration check outs.

Suvarnabhumi Airport Re–Entry Permits are After security but Before Departures Immigration Zone #2

However, if someone were to have went thru Departures Immigration Zone #1 or Zone #3, then they have to tell the Immigration Officer that they want, need a Re–Entry Permit, so for Immigration Zone #1 + Zone #3, Re–Entry Permits are physically After Immigration and directed to Zone #2

so, to make things straightforward, with your Boarding Pass, go to Immigration Zone #2 and Re–Entry Permits will be After security, but Before Immigration Zone #2

Suvarnabhumi Airport Re–Entry Permits

Re other comments, I'm pretty sure it is after immigration desk, as I remember being a bit concerned that I had to actually leave before getting my re-entry stamp.

Use International Departures 2 and the desk is after security but before the Immigration desks to stamp you out

Depends very much on how busy they are. Shouldn't be bad this time of year, but I always leave myself an extra 30 minutes in case they get a rush. Go through passport check 2. You can get there if you go through the other passport control gate, but have to tell the immigration officer and backtrack so it's more of a hassle. At the airport they charge a couple hundred baht extra for form and photo fee. I think it's 1800 (2000) for single reentry and 3700 (4000) for multiple. It's after the security check but before you go through the passport control point. You'll see it at the bottom of the escalator to the right after you go through security.