you just need something solid like a floor joists to nail it to.
If originally they used a full sheet (4 x 8) and there is a wall dividing the original sheet, all you need to do is to cut out a square up to the wall. I would cut alongside the floor joists.
I would be careful with the recp. saw and make sure that underneath there aren't any pipes, cables, or wiring that you could cut through.
I like using a circular saw and setting the depth to the depth of the flooring and cut it out.
Anyway, alongside the joists, you need to screw some 2 x 6's alongside the joists, called sistering, for something to nail or screw the new flooring to. The section must be sound and no bounce or bow when you stand on it. If there is, cut some 2x's to go perpendicular to the floor joists for added support.
Again, screwing the boards down is better than nailing. use galv or zinc coated screws so they won't rust in to.
Where the joints are on the new sub floor, you can apply floor levelor to fill in and make smooth.
This is not a difficult project, the hardest part is cutting out the rotted wood section.