Staying dry in a rain jacket requires you to sweat less moisture than the cloths you are wearing can breath out.
The most effective way to let moisture out is ventilation, unfortunately, that means holes big enough to let water in -e.g. cotton. With a rain coat, apart from wearing it open, Pit zips (zips under the arms) are a very effective way to get a lot of ventilation without letting too much water in (even some very good breathable jackets have them.). The extreme form of a well ventilated rain coat is an Umbrella :) .
The alternate is what are known collectively as breathable fabrics that let water vapour though the fabric, but not water. Goretex is probably the most well known as it was the first to be widely commercialised (It came out of the NASA space program), but there are many others now.
Choosing a fabric is really a trade off between breathability, water proofness, robustness, and cost. Choose three, accept the fourth. Goretex has different fabrics suited for different tasks, with different pricing.
Humidity significantly affect how breathable a particular jacket is on a given day. If humidity is high and its warm, forget about staying dry, even the very best jacket will not breath enough and you might as well wear nylon (or nothing). If its cold and dry, even a cheap breathable jacket will breath well enough to keep you dry. If the outer layer has water build up on it, the jacket won't breath - new jackets have coating (DWR) that makes the water bead up and run off.
In the end, some days you are just going to get wet, and the only thing you can do to stay dry is stay home. The more you spend, the fewer of these days you get. Some days, its just as easy to leave the raincoat at home and wear cloths that keep you warm even if you are wet.