Materials you'll need:

Timber wedges and blocks
Wood glue
Finishing nails
Graphite powder or talcum powder
Chalk
Wood filler
Raw plugs
Wood screws

Tools you'll need:

Hammer
Nail set
Screwdriver.

Squeaky floors are nearly always caused by two loose bits of wood rubbing against each other. It you can locate the squeak, the simplest way to cure it is to puff some graphite powder (or even talcum powder) between the boards. This dry lubricant does not stop the boards from moving but it does eliminate squeaks. For a more lasting solution, try some of these.

1. If you can get underneath the floor, have a helper walk across the floor so you can locate the squeaky spot. Mark the spot with chalk, and hammer in a wedge between the joist and floorboard to stop the boards from moving. The wedges can be made from scrap timber. If wedges alone do not do the trick, try using large wood screws to pull the flooring and sub flooring (bearers) together, but ensure screws are not so long they go through into the room above. Most bearers are hardwood so you'll need to drill a hole first. If you can't get underneath the floor, the problem can still be solved from above.

2. Drive finishing nails through the cracks in the flooring at points around the squeaking boards. First drill small pilot holes in the hardwood then drive the nails in at an angle so each nail goes through both the two adjoining boards.

Staircases.
If you are able to get under the stairs the best way to stop the squeak is to pre-coat some timber wedges with wood glue and hammer them home between the treads and stringers causing the squeaks. If blocks under the treads are loose, hammer them back into place or glue and nail new ones into position. If the stringer has worked loose from the wall, use raw plugs and screws to fix it back into place. Check for any other loose nails, split boards or other problems and fix them.

If you can't get under the stairs try tackling the problem from above. Once you locate the squeak, squeeze graphite powder or talcum powder into the joints around the squeak. You can also drive finishing nails into the offending treads. Angle them so they will go into the riser or stringer where the movement seems to be occurring. Punch the nail heads below the surface and fill the holes with wood filler.