If I want to reclassify to 37F and go back on AD, how will the selection process work? What happens if I fail to get selected?

Don't enlist as a 37F, you probably won't make it through the course and then you'll be stuck with a five year contract and be reclassed to the needs of the Army. It even says in your enlistment contract that you will be reclassed and reassigned to the needs of the Army

Instead, join as an MOS you want, or in your current one, then go to 37F selection as soon as you get to your first duty station. If you pass, you go to the Q Course, if not you go back to the MOS you chose.

Duplicate thread - https://www.rallypoint.com/answers/needs-of-the-army

Since you weren't a 37F before, you'll have to go to AIT*, however you won't actually be scheduled to attend until you have an interim secret (I assume you don't have one since a combat engineer MOS doesn't require one. If you do, so much the better).

You will have to meet with an active duty recruiter and go through all the wickets obviously and meet the requirements of a 37F* (ASVAB 101+, PULHES 111221+, etc). A large plus is that 37F is one of the high demand MOSes (with an additional $3k-$15k a year for you), so your recruiter will be very encouraged to get you into this MOS.

** Edit ** - See SFC (Join to see)'s response regarding how to go about becoming a 37F on active duty.

MSG (Join to see) - duplicate thread with https://www.rallypoint.com/answers/looking-for-more-information-on-the-psyop-37f-process
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* AR 612-201 (Initial Military/Prior Service Trainee Support), para 3-7 - Prior Service personnel
* Qualification for MOS 37F - http://www.army-portal.com/jobs/psychological-operations/37f.html