Enter the basement or crawl space to evaluate the extent of the damage to the floor joists. When a termite problem is present, it is likely that other joists are damaged. Check for cracks in the crawl space perimeter or above a floor joist that shows water damage. Fix these problems before proceeding.
Measure the length and width of the old joist. Joists come in standard sizes of 2-by-8 inches, 2-by-10 inches and 2-by-12 inches. Depending on the construction method used, a particular joist might have a block brace under it.
Take your measurements to the hardware store. Buy two boards the same width and length as your old joist, and four joist hangers to fit them.
Rip the new boards with a circular saw to get a custom fit; the new lumber may be a slightly different size than the old joist. Cut 3/8 inch off the bottom corner on one side of the new joist, using the circular saw set at a 45-degree angle. Cut 3/8 inch off the top corner on the other side of the new joist in the same way. This will give you some wiggle room when installing the joist.
Line up the new joist next to the old joist. Lift it into position. Make sure the replacement joist sits firmly on the sill plate. Tap the joist gently into place with the hammer. Slip a joist hanger on each end of the new joist.
Attach the joist hanger to the replacement joist and the sill plate by hammering 16d nails into each hole in the joist hanger.
Insert the second replacement joist on the other side of the old joist. The old joist will now be sandwiched between new wood. The new wood will be attached to the old wood after the old wood is braced.
Lay a scrap piece of lumber across the jack plate of a hydraulic jack. Position the jack and the scrap wood under the break in the joist. Jack up the joist slowly, repositioning it as you go. You want to fit the joist back in its old spot to be mended.
Apply wood glue to the replacement joist to minimize the squeak of new wood and create a tighter bond. Nail the second replacement joist to the original joist. Offset the nails mending the two joists together. Toenail -- hammer nails in at an angle -- any brittle wood to prevent splitting.
Place new braces under the replacement joists if the original joist had them. Insert scrap pieces of wood -- such as two-by-fours or plywood squares -- as shims on top of the brace if you can see gaps between the brace and the joist.