A razor dries the skin, an epilator makes the skin feel tight, hot or cold wax attacks the skin... whatever method of hair removal you prefer to use, the surface of the epidermis is well and truly abused. A few hours afterwards, or sometimes even days later, the skin can become dry and red, it can feel thicker, pores are more visible and spots appear... In short, we need to calm and gently regenerate the hydrolipidic film of the skin, so we can really get the smooth hair-free look we are aiming for.
The golden rule to immediately calming the skin is to cool it down: a cold application will soothe irritated skin and relief will be instant. So, just after hair removal, spray the affected areas with cold water or apply a cold compress. Then hydrate the skin by using a product rich in soothing ingredients; products that have a brilliantly soothing effect include almond oil, aloe vera, chamomile, jojoba oil or rose water. Also, think about using an alum block; these crystal-like stones are known for their antiseptic properties and can soothe irritated skin.
Make sure you give your skin time to recover between hair-removal sessions. The best way to do this is to avoid products that contain alcohol (some toners, for example), which can cause a burning sensation and further irritation. Wait a few days before using an exfoliator (ideally this should be done before hair removal anyway). And stay out of the sun for at least 24 hours after hair removal.