The radiation is an inseparable part of Fallout 4 and you must deal with this impediment almost on each step. You can be radiated mostly by entering a radioactive territory. It can also happen due to attack of a radioactive creature or when you decide to eat radioactive food. The game always shows information in the corner of the screen about how much radiation you will receive. If it is possible, try to react to it quickly, for example by retreating from a dangerous territory or using equipment items described below.
Two chemicals are best to be used to get rid of the effects of radiation - Rad X and RadAway. Rad-X allows temporarily increasing character's radiation resistance and it is best to use it before entering radioactive area or before starting a battle against radioactive creatures. RadAway is used for getting rid of radiation you already have. It is a very important matter since the radiation is "taking" part of character's health. You should decide to use RadAway when you will lose about 1/3 - 1/4 of health bar. You should also remember that after you heal of radiation, you should use Stimpak or eat something in order to regenerate the lost fragment of the health bar.
If you plan longer expeditions through areas with high radiation, you should equip yourself with other items that will provide you cover from high radiation much more effectively than the Rad-X chemical. One of such items is the Hazmat Suit which offers 1000 protection units. This suit can be found in the game world (for example, in the Cambridge Polymer Labs location) or bought from some merchants. If you decide to use the second option, the easiest way is to go to the Diamond City Market and visit the Fallon's Basement shop (screen 1). In the basement you can trade with Becky Fallon and she has, among other items, Hazmat suit in her offer (screen 2). Using the Hazmat Suit gives you one important disadvantage - it has no other protection values. It means that you can die easily if you are attacked by monsters or bandits. You should decide to wear the suit mostly once you have cleared the area and you only plan to easily reach selected treasures.
A perfect way of dealing with radiation is using Power Suits. The suit doesn't give you 100% protection from the radiation, but the protection is sufficient to avoid having to regularly use RadAway. In difference to the Hazmat Suit, you don't have to worry about whether you will be helpless when attacked by monsters. In addition to that, the Power Suit increases the general defense level. First Power Suit is obtained at the very beginning of the game, more specifically while helping Minutemen in the Museum of Freedom in the city of Concord. If you don't have any suit left, you can for example visit the Robotics Disposal Ground location in the northern part of the map - a suit is standing on the road south from it.
Important - To work, power suits require fusion cores which can be found in many larger locations of the game world (they are used as power sources). Try to have always 3-4 spare cores with you. You don't need to change them manually - every time a core is fully used it is automatically switched to a new one.