Clogged hair follicles are the result of oil produced by the sebaceous gland, dead skin, dirt, cosmetic and hair products. Those substance get inside the pore where the follicle grows, entrapping the follicle. Fortunately, they are treatable.
Washing the scalp and skin daily is the most important part of treatment for a clogged hair follicle. Wash the hair with a clarifying shampoo and wash the body with a soap that does not contain excess oils.
Dead skin is also a problem. Use commercial scrubs on the face daily or go to a dermatologist for a dermabrasion treatment.
Use a skin toner such as witch hazel. Use medications that contain ingredients such as benzoyl peroxide or salicylic acid to dry excess oil and rid the area of bacteria.
A dermatologist can prescribe an oral or topical treatment for clogged follicles. These treatments include doxycycline (oral) and erythromycin (topical).
You cannot "pop" or push out the clog in the pore. The area may become inflamed, leading to scarring and infection.