A dominant 7th leads to a major 6th and a major seventh leads to the tonic, but what does the note in between the two lead to? If you could tell me what the maqam rules for that are, that'd be fine, or in general, but maqams are the only traditional way of using them.
In classical music, sevenths are used as dissonances that demand certain resolutions. For instance, the chord C-E-G-Bb is a dominant seventh chord. The note Bb makes a minor seventh with the C and also a tritone with the E, causing a tension that makes the chord want to proceed to F major.
In maqams, on the other hand, everyone is playing minor variations on the same melody, so tension must be built and released on melodic terms. If there is a neutral seventh (example here) it can freely proceed to either the tonic or the sixth, according as the melody is ascending or descending. If descending, the sixth will have a strong tendency to proceed to the next stabler note, the fifth. The neutral third behaves similarly as a conduit between the second and fourth. Ultimately all notes gravitate toward the tonic (D in this excerpt).