You get training for it starting with practice runs at the NOSC (we had a practice coffin for the flag folding, including how to deal with common mistakes on the fly) and there's an official video too (but no NKO, thank goodness). Next, guys go along and watch from the van a couple times. After that you "play" the bugle a couple of times, posted a short ways away from the gravesite (the distance helps a lot for people who get stage fright). Then finally you are the assistant folder. The lead folder is the one presenting the flag and reciting the spiel to the recipient.
Don't take my word for it but I think you get paid a drill starting when you go along in the van to a service, since you're technically part of that detail.
The expectations are that you're always on time (your show time is something an hour before the party's scheduled time to arrive) and your dress uniforms are squared away (no old, dirty ribbons, no wrinkles, good haircut, etc.). I think there is a small uniform allowance though, but don't take my word for that either.
My experience was similar, but a bit different.
-the FHD coordinator (prob an E-5 at your NOSC) will provide you training at the NOSC.
-You can get ONE training/observation FHD paid for.
-after that, you will be thrown in there—probably as bugler, but many details are only two people, so one will fold and bugle.
-As an officer, you’ll be at the head fairly often (the flag will get folded to you—it’s the easier job)
-As a new officer, you’ll be trumped anytime just about any other O is there, so you’ll get lots of practice folding too.
You’re right to want to do it right. You show up 45 min or so before go-time so that you can rehearse both the movements (every venue is different) and folding the flag (often its already folded...and the wrong way!)
At least in my area it was a little bit of a good old boys club, where the FHD cord seemed to pick her favorites. The other NOSC in my area was “first to reply”, and my old NOSC CO wouldn’t let E4 or above do more than one a month. Just be prepared for possible inconsistencies there.
I ended up doing about 250 services before I retired, and it was probably the most rewarding thing I did as a reservist.