Sweep the floor, and check that all screws or nails sit below the surface. Drive in or countersink any protruding fixings, ensuring that they don't go right through the floorboards and into any cables or pipes beneath them (Image 1).
Check whether any floorboards are loose. If they are, screw them down securely, because a subfloor must be laid on a rigid floor surface (Image 2).
Pick a corner that is as square as possible for your starting point, and lay the first board (Image 3). Use grab adhesive for extra rigidity.
Use ring-shank nails every 6 inches around the edges of the board. Nails should go into floorboards but not through them (Image 4). (An alternative to nailing thin ply is to use a staple gun)
Apply nails every 6 inches in a grid across the center of the board, as well as around the edges, to keep the subfloor level and firm (Image 5).
Butt-join boards tightly (Image 6). Continue laying boards. If boards need cutting to fit, use a panel saw for straight cuts, and a jigsaw for templated cuts.