With leg sinew I throw them in a bucket of water after cutting them out. I'll rinse them off to remove any blood or hair. Then I'll lay them out on a board or a plastic tub lid in the sun if possible. Once they are dry and a nice amber color I'll put them on the head of a sledgehammer and pound them with a smaller hammer to break up the fiber bundles. Then I'll start pulling them apart until the fiber bundles are small enough to be used to back a bow. I'll sort them to length and make a bundle using bread ties on each end. I store them in a small tub in my closet.
For back sinew I'll let them soak in water overnight to loosen any meat left on them. I take a knife and scrape all the fat and meat off of the sinew. Then set it out in the sun and it will dry very quick. Check out Bryce's sinew backed yew build-a-long to see a good example of how to process back sinew.