Your best source of dry air is your freezer.
Let me briefly explain dewpoints and relative humidity.
Water has a
vapor pressure which is a function of temperature. Basically the vapor pressure is the pressure at which water will boil at a given temperature. At 212F = 100C the vapor pressure is 1 atmosphere. Below that temperature it is of course lower.
Let's take a temperature of say 20C = 68F. At that temperature the vapor pressure of water is about 2.3% of atmospheric pressure. (water will boil at 0.023atmospheres) So if you sprayed water at this temperature through the air (at 1atm) the humidity would reach 100% saturation and roughly 2.3% of the air would be water vapor.
Now take that saturated air and heat it to say 30C (86F) where water has a vapor pressure of 46.7% of 1 atmosphere. That air would still be 2.3% water but that's only 5% of the total saturation level at that temperature, so the
relative humidity is 5%.
So to dry air there are three processes you can use.
1.) Compress the air (and allow it to cool to room temp) so that the vapor pressure of water is a small percentage of the total pressure; the excess will condense out. (This is why you must drain compressed air tanks periodically). This is the least efficient method.
2.) Cool the air (say to -22C is the triple point and you get near zero vapor pressure there) and let the moisture condense/freeze out. Then re-warm it. This is how room dehumidifiers work.
3.) Use a desiccant or other chemical means.
The best bet is to use a refrigeration stage or collect cold air somehow and then pass it through a desiccant. Desiccants work by surface bonding to the water thereby reducing the vapor pressure. You won't get absolute 0% humidity but you can get close. The question is how dry do you need the air to be? What is your application?