Hephaistos is a god I respect a great deal but interact with very seldom – things like levees fall under his purview, and I am a big fan of levees, but I don’t build levees myself, if that makes sense. So this is mostly research-based.
Hephaistos’ relationships with Zeus and Hera vary in different myths/cultic centers/parts of Greece. For someone who actively worships Hephaistos, I imagine these relationships might be rich avenues to explore.
Hephaistos was frequently worshiped and celebrated alongside Athena, as they both rule over art and crafts, both useful and beautiful. Several festivals honored them both, and Athens’ origin myth of Erichthonius contains traces of a possible romantic/sexual relationship between them that was lost or discarded as the religion developed. The version of the myth that survives features Hephaistos’ spilled seed impregnating Gaia, who gave birth to Erichthonius, whom Athena then fostered.
Hephaistos was a friend and companion of Dionysos, and when the two of them are depicted together, Hephaistos is attended by satyroi and nymphai, just like Dionysos is. I don’t have any personal experience with this relationship/this side of Hephaistos, but others might.
In his forge and palace, Hephaistos was attended by the Kourai Khryseai (two animated golden statues he had made). He has other attendants as well, most of which are associated with a specific forge (usually a volcano or mountain). Thus, the Kabeiroi are his twin sons on Lemnos, while the Palikoi were his twin sons on Mount Aitna. The Kyklopes and their sons also worked with him on Mount Aitna. Kedalion was an attendant (mortal?) in the forge on Lemnos. Personally, I would speculate that this is a myth-piece that would easily change according to local cultus – the Kabeiroi and Palikoi were strongly tied into mysteries and other practices in their respective locales. So I would say, for anyone pursuing a close relationship with Hephaistos, if there’s a mountain or volcano or other place of power for him near you, consider exploring whether he has other workers in his forge and what other roles and aspects those assistants might have.
Hephaistos was married to Aphrodite, and it went poorly. I subscribe to the thinking that she left him (ended their marriage) to pursue her relationship with Ares. There are doubtless other versions of their relationship.
Hephaistos was married to Kharis/Aglaia. Aglaia is one of the Kharites, and her name means splendor, beauty, or magnificence. I subscribe to the thinking that the goddess’s name is Aglaia, and Homer called her Kharis as an epithet; others may come to a different understanding. Hephaistos and Aglaia had four daughters: Eukleia (good repute/glory), Eupheme (acclaim), Euthenia (prosperity), and Philophrosyne (welcome). These were called the younger Kharites and are sometimes depicted as attendants of Aphrodite, especially Eukleia. I personally find it very telling that Hephaistos is married to Beauty and fathers all these features of an excellent reputation. Very artist-y.
Hephaistos forged weapons and armor for many of the other gods, plus thrones, jewelry, etc. It is not inconceivable that he might be worshiped alongside plenty of other ‘major’ deities.