Comparing two charts
Lay one chart over another and read the angles between them.
The contacts that matter
Sun-Moon contacts describe whether two lives fit together. Venus-Mars describes chemistry. Moon-Moon describes whether you can share a kitchen. Saturn contacts describe whether it lasts. Everything else is detail.
House overlays
Where one person's planets fall in the other's houses tells you what role they play in your life. Your Venus in someone's 7th house makes you feel like a partner to them, whatever you intended. Their Saturn in your 10th makes them a mentor or a critic.
Reading the scores
Chemistry counts Venus, Mars and Pluto contacts. Ease counts easy aspects between personal planets. Durability counts Saturn and Moon links. Growth counts the hard aspects, because those are where the relationship does its work. High everything is rare and not necessarily better.
Composite and relationship charts
Beyond synastry there are charts of the relationship itself: a composite chart made from midpoints, and a Davison chart cast for the midpoint in time and space. They describe the relationship as a third thing with its own temperament.