There is lots and lots of information on this forum about this topic. Once you get a couple of the terms from responses here, I recommend using the search function and pulling up some of the threads that go into details about some of the various means by which folks have dried out their compressed air. That said, in short:
- Drain your compressor daily. This will not help much/at all with keeping your air dry, but it will prolong the life of your compressor.
- water traps and dessicant filters do work, but to maximize their efficacy, you need to cool the air as much as possible before it reaches the drier/filter. Simply put, this is because cool air can't keep as much moisture in suspension (all else being equal) as warmer air so the moisture in the air condenses into liquid water, which the traps are more effective at capturing. There are many ways to do this. This list is not complete, but it is roughly organized from least to most effective (and also from least to most expensive):
- Running the air from the compressor tank outlet through a length of pipe. The idea is that the ambient air temperature (and thus the temperature of the pipes) will be cooler than the air coming out of the compressor so they will act as a heat sink to remove heat from the air.
Pipe materials that have higher thermal conductivity and/or higher thermal mass (or the best combination of both) will be more effective, but will also be more expensive. Copper is great, but is expensive, aluminum is good and there are several commercially available aluminum pipe systems made for this purpose (rapidair's fastpipe is the most common) steel, such as black iron gas pipe is popular and all the pipe and fittings are available at most hardware stores.
The length of you pipe system is important. If you have a big shop and you have 50 foot runs along 3 or 4 walls as part of your distribution system, that will probably be plenty. But if you have a small shop, or if your point of use is near your compressor, you may need to introduce extra length by running "laps" with your pipe before your trap. That said, buying extra pipe just to cool the air (rather than it doublong as your distribution system) can add cost quickly and you may be better served by looking at one of the other options.
One last point with this approach is that you need to add places to drain the water throughout, and ideally, you are constructing your pipe system in a way that the water is encouraged to drain toward a low point. It's easier to capture and drain water from the pipe system than to pump it all into your trap/filter. You will quickly saturate your filter otherwise and it won't be as effective.
- Another option is to cool the air using a radiator as you mentioned in your post. This form of aftercooler is kind of passive in that you are typically using air flow from the flywheel to pull air through the radiator, so you're not powering it separately. Ideally, you plumb the radiator in between the outlet on the pump and the tank so the air is already cool as it enters the tank and the water can condense into tank rather than downstream of the tank where it will need to be trapped and drained out again anyway.
One additional measure can be to add a water trap after the radiator but before the tank so less water is collected in the tank. This is a great option requiring minimal space, no additional power, and minimal investment (these radiators are fairly affordable in the context of an air system) but do require so plumbing/mounting and you will still never be able to cool the air down below the ambient temperature.
- Another options is a refrigerated air drier. This is exactly what it sounds like. The air is pumped through a separate refrigerated unit requiring its own electricity. The advantage is that you can cool the air down well below ambient temperature allowing even more moisture to condense out. The disadvantage is that these driers can be expensive and consume additional power. They are also typically larger and heavier than a passive radiator so you will need more space to mount it on or near your compressor. They will also require a bit of plumbing to install.
Only you can decide how dry your air needs to be based on your needs, but sandblasting does benefit from drier air. Also, as other have mentioned, the temperature and humidity in your shop will determine your starting place in terms of how much moisture is in your air to begin with.
Good luck!