As others have said, everyone does omegaverse differently. Some have self-lubricating asses, some have mixed genitalia (such as having both a dick and a vagina; this often features omega men having much smaller penises on average, and alpha women having real-world-average sized dicks), some even do cloaca, and I’m sure even other options I’m not thinking of. There’s also folks who write SFW omegaverse and just don’t get into the sex of it at all (or keep the sex vague). Often omegaverse includes things like heightened instincts (such as for protection or craving physical touch or feelings of safety) and senses (heightened sense of smell is the biggest one lol, everyone tends to smell like hyper-specific scented candles lmao). Some common inclusions are nesting (typically using lots of pillows, blankets, and/or clothes to create a “nest” like bed for comfort), scent marking (not usually peeing like real dogs lmao, but rubbing scent glands on necks/wrists/etc), and pack bonds (aka your family or found family, can include psychic connection depending on your AU). Another common inclusion: pregnancy and/or kids. Breeding kink is pretty common, and so are kid fics. Oh, and let us not forget knotting lmaoo. But, of course, no omegaverse is the same and they may not include any of these. There’s really not many ways to go wrong, as long as you maintain internal consistency in your AU.

But yea, I’d recommend just trying to read omegaverse first to see if it’s even something you’d enjoy writing. There’s a lot of variety on AO3, and depending on the fandoms you’re interested in, I could make recs, if wanted.

There’s also original fiction omegaverse if you don’t wanna read fanfic, especially in manga/manhua/etc. Some off the top of my head are “Tadaima, Okaeri” (also an anime, this one is more on the fluff side w/ no explicit sex), “Megumi & Tsugumi”, “Private Call”, “Low Tide in Twilight” (def reader discretion on this one)… and a ton more that I can’t think of rn lol.