I have been working on the idea of a mammal following an evolutionary path similar to whales, which started as semiaquatic before becoming fully dependent of its underwater enviroment. So how could a primate, either an ape or a monkey, evolve in a fashion like this, and what traits would it likely have?
I remember reading about a decade ago about something called the "Aqua-ape theory" which posits that either man is an inbetween of apes to aquatic primapes or we have an ancestor that made it back to the water before returning to terrestrial life.
The idea was to explain why despite sharing a 98% genetic commonality with Chimpanzees we have noticeable differences. Humans are capable of storing fat better than apes and our largely hairless nature made the proponents of this theory consider a possible aquatic adaptation over apes. Among our primape cousins, we are way more boyant for our size (a chimp will sink) and the the articulation of our limbs and the noticable lack of fur compared to our relations (our skin is also more like fully aquatic mammals than it is with many hairless land mammals.
So basically, an aquatic primate is going to look more human like than a monkey. If you want the fur, I would suggest otter fur (which has waterproofing for insulation) but again, monkeys and apes are very much not designed for swimming. I can only recall the Japanese Monkeys that more doggy paddle in small pools than actually live under water. Apes simply do not have the limb rotation to do much of any of the more complex strokes.
You'll also have to work out their breathing and sleeping... this boils down to are they amphibious or are the fully aquatic. In the former case, you'll probably want a human like nose or something that can seal up for long periods of time in the water in addtition to lung capacity (which is related to density of objects that push oxygen into the bloodstream, not necessarily body size. They will probably be sleeping offshore or tied to kelp/seaweed like an otter and will swim with a breast stroke while underwater but could be capable of free-style swimming at the surface.
In the later case, you'll want to arrange nasal passages similar to a dolphin and consider gills or an extreme lung capacity. Fully aquatic mammals tend to half sleep so they can unconsciously surface while resting hire brain functions. They will probably be swimming almost exclusively in a butterfly style stroke.
A note on swimming styles: The four competative strokes are Butterfly, Backstroke, Breast Stroke, and Free Style. A Buttefly looks like a dolphin swim, but for humans as is, its horribly energy inefficient (which is why in competitions where the racers use all four strokes, it is first... you can easily do the remaining three with less energy expenditure than the first one). Much of this expenditure is spent pushing the body high enough out of the water to breath, so if your ape's nostrils are higher on their head then this makes it more efficient. The kick is still quite powerful and the best for single direction movement underwater.
The backstroke is the most energy efficient swimming style for surface swimming for humans as it does not cause oxygen loss. It's essentially a free style on ones back.
Breast stroke is probably the most efficient use of the human body for an underwater setting as it combines wide arm and leg motions to displace the most water. It's also called the "Frog Stroke" as you'll look like a frog while peforming it, but it allows more control of multi-directional movement than the butterfly.
Finally, we have free-style (also the front crawl). It's the most human way to swim and can out pace any stroke on the surface for speed. It's a complete waste under water as the chief power relies on pulling the water with ones arms rising partially above the waterline. If you had a more dolphin nasal configuration, this would make it much more reliable as it the arm movement on your stomach is much more powerful than on your back, but you still have to take breaths... nostrils higher on the head would mitigate that problem.
Most human strokes rely on a foot componant and the quickest way we increase our swim speed is the flipper, which increases the surface area of our propeller and thus the water displaced. There are also gloves with webbing to do the same for hands, but they don't have the advantage. You'll probably want to look into a wide, webbed foot and hand, but not so much that they look ridiculous if they will be going on land... flippers are awkward to walk on land with, but there's little loss for webbed hands. You'll also want to look into how mammal eyes work underwater as human eyes are not suited for such conditions.
Hope this helps.
There are plenty of mammals that are very or entirely aquatic: otters, beavers, platypuses, dolphins, whales, etc. There are also aquatic lizards and aquatic turtles. Although these animals are quite different, they share a surprising trait: none of them have gills! They breathe air, with lungs, just like land animals. So, there seems to be an iron-clad evolutionary rule, that gills never replace lungs. (Even with amphibians, this is true.) Instead these aquatic animals can hold their breath for a long time, which is key to their survival. I would make that your first rule: Your aquatic apes develop ways to hold their breath longer and longer. Study how these other animals do it, and copy their adaptations for your sci-fi "sea apes."
Other commonly-found or possible adaptations: webbed fingers and toes; some way to prevent hypothermia (either thick oily fur or a layer of blubber); ability to locate stuff underwater (either sonar or whiskers); ability to communicate while underwater (e.g., using clicks); an especially strong epiglottis to prevent lungs from taking in water (??not sure about that??).
As far as how they could evolve in this way: they'd have to start out as shore dwellers, and proceed from there. And there'd have to be some strong motivation driving them from land (and/or drawing them to sea). Apes are already well-adapted to live on land, so you'll need some really strong selective pressure to turn them aquatic.