At first you can't tell which areas are radioactive, but the placement of radioactive areas is semi-logical. You would expect military areas to be the primary targets of nukes, so anticipate them being radioactive in Ravage too. There are also plenty of other places where you'll find radiation of varying strength.
The longer you stay in a radioactive area, the more radiation poisoning you'll accrue. Once you get over a certain level of poisoning, you'll get ill and start to lose health. When this happens, you'll see a fuzzy effect across the screen.If you can find a Geiger Muller counter, it will really help you. Open your inventory and double-click on it to turn it on. You'll get some text on the screen telling you it's on. Now whenever you're in a radioactive area, it will emit a clicking noise and you'll see a numerical value in the bottom right of the screen to show how much radiation you're absorbing. Note: this is the amount after any protection you're wearing is taken into account. You can now see the cumulative amount of radiation poisoning in the top right of the screen when you open your inventory. It's listed as Rad Exposure.
Speaking of protection, you can find an wear certain items that will help protect you against radiation. None of it will make you radiation-proof, but it will reduce the amount you absorb. The only items of clothing that can help are the pilot coveralls and CSAT high-tech gear. The gas mask also helps reduce exposure.To cure radiation poisoning you need Anti-Rad pills. You can find them as loot in buildings and some enemy AI units carry them too. Once you've got some pills, open your inventory and double click on them. You'll see a notification confirming you've taken one. If you have a Geiger Muller counter, you'll see a value in the bottom right of the screen indicating that your radiation level is decreasing. It takes time to go down - it's certainly not instant. After a few minutes, the pill finishes its action and you can take another.
When your radiation exposure gets above 35, you'll see your status box say Radiation Poisoning and you'll start to (slowly) lose health. By taking Anti-Rad pills, if you can get your Radiation Exposure back below 25, you'll no longer have radiation poisoning.
Certain items of food and drink contain radiation and contribute to your Rad Exposure. Dirty water is radioactive, whereas clean water is not. You need to take this radiation into account when deciding what to eat and drink.