You can hit 'lookup in browser' in Picard, and then search the database/website manually. Clicking the green 'tagger' icon should add the release to Picard for you.
You can then drag and drop your files (on the left hand side of Picard) into the right item in the database (in the right hand pane).
edit: or just paste the musicbrainz release URL into the search bad
A few notes:
You can edit the database - please correct any mistakes you find
But please take note that MusicBrainz strives to document music releases as accurately as possible. This means that sometimes, in order to reflect a specific release as accurately as possible, we might sometimes have information that is technically wrong, but was released that way (by the label or whoever originally released the item).
Meaning: if the cover art credited 'Frank Herbert', we might leave it that way in the database.
That said, we do fix some things, for instance if the track order is printed wrong on a CD, so this isn't a concrete rule - but something to keep in mind.
This just means that something, or multiple things, don't match up between your file and the database information.
Probably the existing tags don't match, which is fine. Just make sure they're being re-written to something you want (check at the bottom)
And for the rest, don't forget that you can drag and drop files to manually match them!
Hope some of that was helpful, can be hard to guess the problem from a forum post!