So I've been thinking of adding a hardwood floor in my dining room and hallway. This is what I know as of right now. I have Hemlock 2x10 Floor Joists spaced apart 16" OC that span 13 feet and the home was built in '71. The subfloor as it sits right now is 1/2" plywood with what seems to be 1/2" MDF or Particle Board nailed on top. I've noticed the floor is not perfectly level and might be due to the MDF warping and expanding from moisture. From what I've been researching it would be best to rip up the MDF (or Particle Board) and gluing the 3/4" plywood and screwing it down to the existing 1/2" plywood (not to the floor joists). Then lay down a vapor barrier and then the flooring at a right angle to the floor joists. Is this correct? I just want to get all of my ducks in a row before I go spend money.
I have seen 3/4" thick hardwood floors go over 1/2" subfloor with no problem. Your floor structure is plenty heavy to carry any load you apply to it. In many older homes (really old homes) there was no subfloor at all, and the floors held up very well.
Remove the layer of MDF, clean up the nails, and reset all the nails that are in the subfloor. This minimizes the chance of squeaks from the nails that may have risen up as the framing dried and shrunk. Add 1 5/8" screws at all the edges and 3 or 4 more spread across the center of the spans of all the plywood.
In my humble opinion, DO NOT use an underlayment foam under hardwood flooring. This is only intended for floating floors!!!!. The "give" the foam has, is asking for your floor to squeak!!! The only vapor barrier you need is a 5 lb. felt paper. It is much lighter and much thinner than roofing tar paper and will give the resistance the wood needs against moisture rising from below. This is what is used in all new floor applications. Sometimes, on occasion red rosin paper is used too, I believe it is error, it has no resistance to vapor permeability.
After this initial bit of prep, lay your new floor.
The best idea would to start by ripping up the MDF assuming the plywood underneath is good and not rotten or destroyed, then check the floor to see if it is level again, if it is you can put down new 3/4 plywood and screw it in, there is no need for glue here. I would recommend screwing it into the joists though, not just the plywood! Then lay down your vapour barrier and hardwood foam if you want to (I always do, it's quieter that way) and then lay down your hardwood like any other floor!
I voted up Jack's answer since he is right on with everything. Just want to add that you are not doing your whole house so you need to figure out if taking out 1/2" MDF is going to affect the height matching of the adjacent flooring. You may very well have to put back a 1/2" sheet of plywood after ripping out the bad stuff.