Species. Most agree merpeople are some strange mix of mammal and fish. You should probably determine to what extent merpeople are one or the other.
Merpeople are typically portrayed with human-sized bodies. There’s no need to do this. Water can support merpeople as big as whales and as small as seahorses, and everything in between. However, huge merpeople will not haul themselves onto rocks to lure in sailors - their massive weight would collapse their lungs.
In addition to the tail, merpeople would have additional fins for stability. Their hands are probably webbed to help them push through the water. They have a dorsal fin to maintain stability. They will also have small fins on their tail, again, for stability.
Freshwater fish and mammals tend to be drab (brown, green, black) to help them blend into the dark water. Reef fish are brightly colored. Fish and mammals on the open ocean are blue, black, or silver. Environment will influence your merperson’s tail color.
Reproduction is a crapshoot. Merpeople could have reproductive organs in the style of fish, cetaceans, or humans. In the latter case, stories have had merpeople pull down the top part of their tail to reveal their human genitalia. If your merperson’s organs are based on a cetacean’s, you’ll notice a cetacean’s mammary glands are towards the base of their tail. I suppose you could put human breasts on a female mermaid if you excluded these glands, but breasts create drag and having them would be a detriment to survival. If you give a fish-like female merperson human female breasts, I will come after you with a knife.
I mean location in three different ways: saltwater, freshwater, or both; ocean zone; and temperate zone.
Say you’ve decided the merpeople live in the ocean. Please don’t just say “the ocean”. The ocean is a big place.
Most of this depends on how long your merpeople can hold their breath. 20 minutes (how long an orca can hold its breath) will barely get you past the photic zone. The larger your merperson is, the larger their lungs are - and the longer they can hold their breath. Humans have reached depths 1,043 feet with SCUBA gear. The deepest depth a dolphin reached was 990 feet. It seems that oceanic mammals rarely need to worry about the bends. Also, if your merperson receives oxygen from the air, it’s likely their lungs are reinforced to prevent collapse at deep depths.
It’s easiest to live above the continental shelf: plenty of seaweed and fish, clear waters, and shallow water to hunt in. The open ocean is more difficult: less prey, no obvious directional signs, and more predators. Deep-water merpeople would be horrifying: huge teeth, glowing lures, and pale/transparent bodies would be the order of the day (and this is why someone should write deep-water merpeople).
Polar, tropical, or something in between? Colder areas tend to have more rugged coastlines for merpeople to hide in. Arctic environments would require a thick layer of blubber to survive. Tropical environments have the greatest biodiversity.
With manipulator appendages (hands with opposable thumbs), it’s totally possible mermaids could create a complex culture. They could use rocks as tools, seaweed as rope, and chisel away rocks along the shore to build small structures. However, steel and iron will be beyond them (requiring fire) and underwater construction will be as well (can’t use mud, vegetative matter, or large blocks of stone). Your mermaids could live some of their life on land - like seals - where they have shelters and forges.
Communication would prove difficult. If you’ve ever tried to speak underwater, you know it doesn’t work very well. Dolphins use echolocation and fish use body language and/or color changes. Your merpeople could use a combination of these. My point is that your merpeople will not create a language they can only understand if they must break the surface every time they want to speak with each other. It’s impractical and dangerous. They might learn the languages of surface folk, but that will not be their species’ form of communication.
The ocean is primarily carnivorous. Your merperson will not be threatened by most carnivores - seeing as they eat small fish, crustaceans, plankton, or microscopic organisms - but large sharks, dolphins, and seals will pose a threat to them. Merpeople will also need to watch out for poisonous and venomous ocean creatures. If they interact regularly with humans or other self-aware creatures on the surface, merpeople will need to deal with nets, fishermen, and people killing them to protect their fish harvest. How the interaction happens is up to you: it’s possible the merpeople and land dwellers have worked out a peace treaty or they could be at war, the merpeople drowning sailors and ruining ships, and the terrestrial people stringing nets over merpeople-frequented areas.