First things first
All help is welcome, we lack people power to handle bug reports so don't hesitate to try a few things written here. You'll see it's rewarding to tweak bugs.
Bug reports are designed to help the maintainer to have a better package.
Often team maintained projects have an IRC channel and/or a mailing list for the team. You can use these as resources when you are triaging bugs. If they have an IRC channel you may well find other users around at the same time that you can enlist to try to reproduce a bug you're having trouble reproducing or other people to advise you on issues with bugs.
Upstream normally have a mailing list for their software even if they don't have a bug tracker and they may have an IRC channel too. Again an IRC channel might be useful to find people who can help you to reproduce or rule out bugs.
Search engines can some times be useful resources in tracking down if other distributions or people have seen the same bug.
Different ways to work on bug reports
Browse bug reports
You have many possibilities with BugTriage.
Closing bug reports
The best is to write a patch and wait for the maintainer to close the bug once the package is updated with your patch.
You can also close bug reports if a new version fixed the problem, but remember to say in which version it was fixed.
You can close bug reports that are tagged "moreinfo" since more than a year, if no info has been provided and it seems unreproducible.
Interesting blog post about bug triaging: https://www.chiark.greenend.org.uk/~cjwatson/blog/bug-triage-rants.html