Measure the length of the central joist in the floor from the basement underneath. Make sure you measure to the very ends of the joist, which will be sitting in cutouts in the walls or on supports at the edges of the walls.
Cut the new joist to length you determined in Step 1, using a circular saw.
Set the new joist alongside the old one --- with the help of an assistant --- so the wide sides of the two joists are flat against one another.
Set the ends of the new joists onto the same supports or wall cutouts as the old joist.
Shoot 3-inch screws through the new joist into the old one. Put the screws in sets of three, at the top, middle and bottom of the joist width, and every 12 inches along the length.
Repeat the process for each joist you want resupport. If you're only going to resupport one or a few of them, do it in the middle of the floor rather than at the edges, as the middle is the weakest point.