To solve a bounty:
Click "Solve Bounty" on the issue page
Follow the instructions (fork, clone, code, push, submit PR)
Requesting to solve a bounty
For private repositories, you first need to be added as a collaborator (get directory access) before you can solve a bounty.
To complete a request you upload your resume (unless you've done it before) and sign docs (if the bounty creator has added any).