Through the lungs
I see no reason why we need to change the full body plan. We can make due with what us there and adapt it.
If we try to just submerge us and use gills in the lungs, we'll suffocate. Water hold much less oxigen than air, so we would need to take in more water for the same oxigen. That alone is already enough to kill us, but it isn't all. As water is much more difficult to 'breathe', you'll also exert much more energy for each breath. It would be like doing a full marathon of effort, just to breathe normally.
To improve this, we can start with making the lungs more fish like. Fish gulp a mouthful of water and force it along the gills. I didn't find exactly why they force it, but I suspect good gas exchange between the blood and water only happens well if water flows past fast, as it'll be saturated quickly. If we gulp down water, we can force it out at gills at the lower end of our ribcage. This both increases the throughput of water, as the exit is close to the surface, and decreases the amount of energy wasted by forcing it through a long tube twice. If we follow this further we can decide to have gill 'inputs' closer to the lungs on the ribcage. This does pose difficulties for how the ribcage is constructed. In addition, biology normally reduces the amounts of orifices, as each orifice is an extra area susceptible to infection and such. We can still see that where needed more holes are available, like gills with fish.
If we're already upgrading the ribcage, you could look at a way to breathe separately with each lung. That way you always have a flow of water, letting your beings be oxygenated more equally at all times.
Advantages and disadvantages
Compared to lets say gill hair you have many advantages. The active process makes sure you don't suffocate. Gill hair on the head or body is passive, making it possible that the person will draw the oxigen out of the oxigen in touch with hair and then it isn't replenished, making them suffocate. This can happen during sleep or when doing stationary (heavy) tasks. Even some movement isn't going to help. If this was the case, fish would do it.
The energy needed isn't too high, as you have many gill slits close to the lungs make sure the flow is as easy as possible. This resembles fish breathing more closely as well, which have had many millenia of evolution to come up with good breathing methods under water.
The ribcage needs an overhaul. The gill slits will make the workings of a ribcage or similar more difficult. Possibly they can be installed front and back just under the ribcage. This requires a much smaller amount if work, doesn't interfere with the muscles used for breathing and only marginally increases the length of the tubes to the lungs as well as decrease the total draw in size of the holes.
The lungs can possibly be more flat, allowing for better musculature. This is as volume is less important than flow over the gills.
If the adapted lungs are asynchronous, the oxygenation of the blood can happen more homogeneous. Compared to spikes in oxygenation of the blood this can have many small health benefits over long times.
The fish people do require no clothing at the gill holes, but as they are regionally endothermic this isn't too much of an issue. In addition, the temperature at a certain ocean layer is also very stable, so they are likely evolved to withstand such temperatures.