I have a 62 F100 with 292 y-block, manual 3 speed. Shifter has been moved to the floor (FYI).

1. What transmission do I currently have? My thoughts are that it's probably the Warner T-86, but I'm not sure.
2. Is there a simple bolt on that can give me a an overdrive?

 

There should be numbers on the transmission that can be used to identify it. The VIN plate will tell you what it originally had but there is no guarantee that it is what is installed now.

There were 3 speed overdrives. One for a Y-Block truck should be the easiest to do but possibly hardest to find. Next would be a modern transmission like a T5 but it will be more involved. The price could be pretty similar depending on a lot of variables.