How can one detect (preferably artesian) aquifers nowadays that a lot of sensors are available? Should I use ground-penetrating radars, neutron detectors, or any other advanced devices? Can seismic imaging be used to characterize the extent of the aquifers?
From what @Richard and @JoeKington said in their answers, it seems that the usual way of finding water is through a hydrological map.
However, for the sake of completeness, I'll include here a bit about what geophysical methods could be used to find water. I'll not comment on the practical issue of cost-benefit as that was nicely explained by @JoeKington in his answer.
That said, any geophysical method is only able to detect a contrast of a physical property. For example, seismic methods are sensitive to variations in seismic wave velocity, electric and electromagnetic methods are sensitive to resistivity/conductivity, gravimetry is sensitive to density variations, etc. So for any geophysical method to detect water, there has to be a contrast in the physical property between the water level and the surrounding rocks/soil.
Knowing this we can already rule out gravimetry and magnetometry because there is no significant density/magnetization contrast when we reach the water level. These methods can give you an idea of the regional geologic setting, and that can help you find water. But detecting water directly? Probably not.
The presence of water does have an impact on the electrical conductivity but that is usually not very large unless the water is salty, which I'm guessing you wouldn't want to drink. Methods like GPR and electrical resistivity methods could map the depth of the water layer, but this effect might be masked depending on the soil type (clay might have very low resistivity and that makes "seeing" what is beneath very difficult).
Seismic wave velocity is usually affected by the presence of water in the soil. If all you want is the depth of the water level, then shallow seismic refraction might be a good method for that. Acquisition is relatively cheap and the data are easy process (usually just simple trigonometry).
Most of these methods will not tell you for sure if the water is there or if it is drinkable. However, they can give a bit more insight to complement the hydrological information.
Hydrosource Associates (no personal relation) claims to use the following:
HSA’s use of geophysical instruments and methods includes seismic, electrical resistivity, ground penetrating radar, electromagnetic, magnetic, gravimetric, self-potential, and magnetotelluric.
Since you're looking for a list, you could investigate each of those technologies above.
However, the one instrument not mentioned above and the most high recommended method is simply using geological maps.
I'm not an ideal person to answer this, but that's never stopped me before, so here goes! :) I've helped several hydrologists with the geophysical side of things at various points, but I'm not in any form or fashion a hydrologist myself. My father did the government permitting for residential water wells and septic systems where I grew up, though, so I've seen a bit of things from both the academic side and the practical side.
For locating the average residential water supply well, gephysical methods are basically never used. They're just too expensive compared to drilling the well.
However, for making detailed hydrological models, geophysical methods (particularly ground penetrating radar (GPR)) get used quite a bit. In fact, there's a whole field called "hydrogeophysics" that deals with imaging in near-subsurface environments.
These methods don't get applied for locating a single well. They get applied to build detailed 3D models to constrain things like contaminant transport.
If you need to know how groundwater is flowing in 3D, then you need a more detailed image of the subsurface than you do to locate a single water well. GPR is the most commonly used method, but I've seen almost every sort of geophysical data used in some cases (basically where it's already been collected and is freely available).
Basically, the bigger the budget, the more fancy tools can get thrown at the problem. :)