Place contact tape or heavy masking tape on the window glass to prevent breakage during removal.
Remove old caulk from around the window. Then, use a cat's paw to pry out the nails holding the old window in place, or you can use a reciprocating saw or mini-hacksaw to cut through the nails. Be careful not to damage the sheathing of your home.
Most windows can be removed in one piece, but depending on the type (e.g. double-hung, casement) and age of the window, you may need to remove parts of the window (e.g. bottom sash of a double-hung) before the rest of the window can be removed.