Radiation
Radiation is a process in which energetic particles or energetic waves travel through a vacuum, or through matter-containing media that are not required for their propagation. Waves of a mass filled medium itself, such as water waves or sound waves, are usually not considered to be forms of "radiation" in this sense.
Sources of radiation
Radiation is found predominantly in craters, toxic waste dumps, and toxic waste sarcophagi, but other more unheard of sources also exist; any tile that has contained radioactive gas or the small unmarked craters that dot the New England's countryside are heavily irradiated.
In general, radiation is easily avoided. If for some reason you wanted to scavenge those irradiated locales, its better to keep trips short or to wear protective clothes. Wearing a clean suit or a helmet less suit of power armor will partially protect you; but if you want to loiter the irradiated area for a long time span, its recommended that you wear a Hazmat suit, ANBC suit, or a full set of Power Armor, as those items will confer complete protection from radioactive sources.
Detecting Radiation
Radiation cannot be directly detected by the survivor, but there are instruments with the ability to reveal the radiation level off both your body and of the ground in which you are stepping (the actual advantage gained from knowing the radiation level of a tile after you have been already contaminated by it is questionable). However, because the places in which radiation exists are well know in advance and far in between, obtaining them shouldn't be a high priority.
Radiation Sickness
Radiation sickness in game traduces to a myriad of penalties that start triggering once your internal radiation levels rises past the 80 rads threshold; at this point, you'll suffer a small penalty to movement, the strength stat, and nausea; depending on worldgen options, you may also have a very small chance of gaining mutations by this point. At 120 rads of exposure, you will begin to suffer penalties to every stat. Actual damage to all your body parts and random episodes of pain will begin once your exposure goes past 150 rads. Ultimately, an exposure higher than 500 rads is invariably fatal when left untreated, but with the liberal application of healing agents or with some luck (in the case you manage to mutate several times in a row), it can be survived.
Due to its nature, radiation sickness cannot be directly treated. Your body will eventually recover naturally by slowly lowering its radiation level and this rate can be increased by consuming iodine tablets but even then this it is not very impressive. A specialized CBM exists which will decrease your radiation by 5 rads every time it is activated, but even that may not be enough to save you if you were exposed for a long time.
In short; getting irradiated is probably not a good idea.