How can I extend my one-year O-A visa to two years in Thailand?

You enter in the first instance as close as possible to the issue date of the visa. On day 364 (or a bit earlier) you border bounce and get stamped in for a further 365 days. All on the proviso your insurance covers the relevant period. For the bounce within the validity of the visa you do not need a re-entry permit

You enter Thailand at the end of the Non-OA validity (on or jsut before the valid until date), get the last 365 days entry stamp as long as you meet the insurance requirements. This is so-called the "second year stamp" from Non-OA. Your 'first year' can start anytime after Non-OA was issued, when you enter Thailand for the first time. Every time you enter Thailand after that, you will be stamped for 365 days without re-entry permit until the validity of Non-OA.

Once your original visa expires and if you want to travel out and back Thailand during this last 365 days, you need re-entry permit before you leave kingdom