Measure the rise and run lengths of the stringer pockets, which will represent the width of the tread. Each pocket will form a a right angle (step shape), with one slot representing the run or flat tread, and one forming the riser or the vertical tread.
Measure the distance between the stringer boards, which will determine the length of the treads. Measure from the inside of each pocket when stretching a tape across the distance between each stringer.
Cut the oak treads to fit the width and lengths. For example, if the distance between the stringers are 48 inches, then cut the tread 47 7/8 inches long to allow for wood movement. If the pockets are 8 inches vertical and 10 inches horizontal, then one oak step ( vertical riser), should be 47 7/8 inches by 7 7/8 inches, and the runner (horizontal step) should be 47 7/8 inches by 11 inches to allow for overhang of the step over the riser.
Tap the riser into the stringer pocket first. If the oak wood is too thick, then bevel the edges slightly with a belt sander. Slide in the runner tread in its horizontal position, tapping it slightly with a rubber mallet if necessary. Bevel the edges of the runner if the wood is too thick for the stringer pocket.
Trim out the stringers with shoe molding to cover the gap at the pockets where the risers and runners slide into the stringer. Attach the shoe molding with a finish nailer. Caulk the remaining gaps with caulking to complete the finish.