I received a 1099-misc for prize money won. The amount is $1332. What do I put for Fair Market Value?

Since you received a cash prize, the amount received is also the Fair Market Value (FMV).  TurboTax asks if there is any adjustment to FMV.

If you entered prize winnings from a 1099-MISC in TurboTax, once entered you will see a screen titled "Fair Market Value of Prizes and Awards".  There will be a box next to Adjustment to Value of Prizes and Awards.  Having received cash, you will leave this box blank.  (If you had received an item, there may be a difference between the FMV of the item and what was reported to you.)

See screen shot below.

To get back to the "Fair Market Value of Prizes and Awards" screen:

Once in return:  Federal Taxes -> Wages & Income -> Other Common Income ->  Revisit Form 1099-MISC -> Click Done on "1099-MISC Summary" screen