Measure the distance along the floor of the two pieces of flooring that you need to spline together. If possible, make the spline out a single length of wood.
Measure the width of the grooves in the sides of the flooring. Set the fence of the table saw to cut to this thickness.
Cut a 12-inch long test piece on the table saw. Use a push stick when doing this cut, because the piece is very narrow; trying to do it with your hands would be dangerous.
Fit the test piece into one of the grooves. It should fit snugly but not be difficult to push in and out. If it's too tight, move the fence closer to the blade. If it's too loose, move the fence away from the blade. Cut more test pieces until you have a perfect fit.
Cut the spline tongue out of a piece of wood that is the length of the two pieces of flooring that you are joining. Insert the spline between the two pieces when you lay the floor.