Check to see if the contrib module has a modulename.drush.inc file in it. If it does, then the module provides Drush commands, and you can find out about them via
drush help --filter=modulename.
If the command does not supply any Drush commands, the next thing to do is to open up the modulename.module and scan through the source code, and see if it has any API functions that perform the operation that you want to do. This can sometimes seem intimidating, but it's worth a shot! If you'd like to set the frobulation level of the module to 28, maybe, just maybe, you might find a line that reads
function modulename_set_frobulation_level($value) .... If you do, then you can call it with Drush like this:
drush ev 'modulename_set_frobulation_level(28);'
If you do this a lot, you could make a Bash function for it, or, better yet, create a custom Drush command and contribute it back to the contrib module. Making a custom Drush function is really easy with the drushify command.
If you are unlucky, you will not find a nice set_frobulation_level function; sometimes, the code you want is only available in a form submit handler. This is distressingly common in contrib modules. Rather than try to figure out how to post a fake form submit, an even better option is to just factor out the code you'd like to call, and make the modulename_set_frobulation_level function yourself. Then, it's easy to create a Drush command for it, and you can contribute the whole shebang back to the contrib module when you are done, helping out the next person who travels this same road.
This might sound like a bit of work, but it's no harder than reverse-engineering the sql commands you'd need to run, and the results are much more satisfying.