For the sound quality I recommend two possible approaches:
1) Build the area oversize in case you ever want to upgrade, and stuff around the sub with fluffy insulation (like Owens Corning R30 or something, the pink stuff). This will reduce possible SBIR issues from the sub to the sides of the wall. Also reduce possible diffraction noise.
2) Build it just large enough to fit the sub, this will cause a large baffle wall effect.
Of those I'd go for option 1. Either shouldn't affect the sound terribly. Are you running an AVR with decent bass eq? If so it should be able to easily compensate for either option. It would be way worse if you were embedding speakers due to baffle step compensation, but even then manageable with EQ.
As for how to build,
might have more ideas. Since you'll need to cut your wall studs for this you need to start worrying about structure. You're going to have to frame around it similar to what's done with windows. King stud, jack stud, sil plate, header, and cripple studs. You can google "window framing" to get an idea, but look up the code in your area. Also make sure you know where power cables are so you don't cut them. The usual safety precautions.
Is the theater soundproofed? If so you're going to have to build a fully decoupled backer box to go in the hole. If not, then a box out of 3/4 or thicker mdf, slid into the hole, should suffice. The thicker and more rigid the better. Then nail it to the studs and trim it out as you see fit.
Edit: For this you may get better feedback in the Dedicated Theater Design and Construction section of the forum.