I think the interface only allows reviewers for PRs, and not for issues (though you could always make a comment on an issue declaring your intention to review any resulting PR).
For PRs, you have a couple options:
1. At the top right of the PR, there's a "Reviewers" box, with a gear icon next to it. If you click on the gear, it will show you a bunch of people, with yourself as first. You can assign yourself as a reviewer (and possibly request other people as reviewers). Please let me know if you don't see the gear or the list of people, since this may depend on your role in the repository.
2. If you click on the "Files changed" tab, you can add comments on lines and at the top right there should be a green button "Review Changes".
David