I moved into an older house and have a brand new Maytag Bravos dryer. I took the 4 prong cord off and there is a white wire that was installed under the middle prong of the 4 prong cord. The white wire is part of the dryer... it comes from a bunch of wires inside the dryer. I am now putting a 3 prong cord and all of the directions say you need a "grounding strap" which I don't have. I do however have an "extra" white wire. Where do I connect this? Where it was connected before in the middle post? To the green grounding screw?

With a 4-prong outlet (as required by modern electrical code), there are separate connections for neutral (white) and ground (green). In older configurations with 3 prongs, the neutral and ground are tied together. So you'll simply hook the white wire and the green ground wire to the same terminal on the 3-prong plug.

Ultimately the safer alternative is to replace the 3-prong outlet with a 4-prong, but that would likely involve not only replacing the outlet, but also replacing the wire in the wall (from the 8/2 wire that's probably there now with 8/3 wire).

I agree with above to change outlet to 4 prong, Receptacle is cheaper that the 3 wire cord, and easier to change out.
If not going to 4 prong,
The center needs a strap between the center white(s) and the case Ground screw. I would use #10 to be safe.