I'll break this down into two sections: Basic Survival and Comfortable Living.
Either gills or enhanced lungs/oxygen efficiency.
Gills: Permanent operation underwater. In order to be truly effective, you would also need a way to pull water over the gills without moving. Some species of shark lack this ability, and it results in a need to constantly be moving in order to breathe.
Sticking with air-breathing: Humans are very inefficient at extracting Oxygen from inhaled air compared to dolphins. A human captures about 17% of the oxygen from a breath, dolphins capture 80%. You would then need to increase the concentration of hemoglobin in human blood to allow for greater oxygen storage within the body. It would also be necessary to remove 'breathing' responsibility from the brainstem and move it somewhere that is only conscious. Since breathing would become less common than not breathing, you don't want that wired to the autonomic nervous system. It would also be ideal to develop a way to seal the nose and sever the respiratory system from the mouth so that you could eat underwater without drowning. Increased lung capacity is only so effective, as you will see in the Pressure Regulation section below.
Humans are now immersed in salt water 24/7. Drinking salt water dehydrates humans, so you would need to tweak their digestive system to filter out all that extra salt content and expel it in their urine. Alternatively, some aquatic mammals extract all the water they need through their prey, and don't actually swallow salt water. This would require humans to be able to consume the blood of their food without getting sick on it, and be able to extract the water from that.
We would also need to tweak our dietary requirements. Vitamin C is hard to come by in the ocean, after all. Don't want everyone to end up with scurvy. Additionally, reduced exposure to sunlight means humans would synthesize less Vitamin D. Lack of Vitamin D leads to things like depression and moodiness (oft referred to as Seasonal Affective Disorder). There are a number of other tweaks that would need to be made here as well.
SCUBA divers need to either take numerous stops on their way back to the surface to avoid getting 'the bends', which is what happens if you depressurize a human body too quickly. The structure of the middle ear would need to be altered to protect them during deep dives. You may need to make exhaustive modifications to the nasal structure so that it can freely collapse as well, and not put pressure on the cranial area. Additionally, if an air-breather, the lungs would need to be heavily reinforced (and allowed to safely collapse in such a way as to force all held air away from the alveoli) while deep under water to prevent air-exchange from occurring. This would protect against the insertion of Nitrogen into the blood stream, which is a common cause of The Bends.
The human eye doesn't like salt water, and it doesn't do well with high pressures. It would need to be remodeled to both have a protective lens over it (possibly mobile) to protect it from the salt water, and would need to be reinforced to survive pressure changes.
It would be advantageous to lengthen the toes and fingers of an aquatic human and web these appendages together. This would allow for greater propulsion through the water.
Alterations to arm muscle structure
It is hard to move quickly in the water, and surviving against possible predator attacks is difficult, even when armed. This is because the human muscular structure is configured in such a way as to permit dexterity and range of motion, rather than strength. Either the muscles in the arm would need to be bulked up, or their attachment points would need to be shifted further along the bone, giving greater leverage to the muscle. Bones may need to be reinforced as well to support the increased strain.
While our divers could make due in thermal suits, it would be better to give them a natural way to stay warm while in the cold ocean. A higher metabolism would allow their body to produce more heat, and a subcutaneous fat layer would provide insulation (aka blubber).
Enhanced dark vision
The ocean is really dark once you get down past about 300 feet, and normal humans would need light all the time. Blue light penetrates the deepest into the ocean, so modifying the eyes to be more sensitive to that shade, and tweaking pupil size to allow for more light to be collected would improve the depth at which humans could see
Alternate means of sensing
Beyond a certain point in the ocean...eyes are largely useless for any sort of significant distance. This is why so many aquatic animals echolocate. Introducing this ability to your aquatic humans would greatly improve their underwater comfort at depths beyond which they can comfortably see.
Further physiological tweaks
Many deep-ocean aquatic mammals are capable of voluntarily controlling their own metabolic rates and heart rate. This allows them to put their body into a lower performance mode to conserve oxygen. This tweak would allow air-breathing humans to go on longer dives before needing to resupply.