It only takes a few days to dry. You can tell when it is dry because it is yellowish and translucent. I have dried sinew on my work table in the sun or on top of the frig. Put it somewhere that animals can't get to it or they will. Once dry store it until you are ready to use it.
To use leg sinews you will have to break it up first. With a hammer or round stone pound it until the outer casing splits. Remove the casing and divide the tendons into workable size fiber bundles.