this is one of the things that really should be done by a professional.
i know i gave myself some scars from trying to get rid of blackheads over the years.
wash your face thoroughly with a scrub that will gently exfoliate the top layer of skin. make sure your hands are scrupulously clean!
then half-fill a bowl with boiling water. add something that smells nice - a fresh herb or some dried lavender. drape a towel over your head and put your towel-encased head over the bowl to steam open your pores. DON'T put your head too close to the water, you don't want a steam burn.
after about 5 minutes your skin should be soft enough to extract anything close to the surface.
use cotton pads, like those you would use to take off makeup. using the pads of your fingers - NOT your nails - press against the affected area gently. if the blackhead shows no signs of coming out, it's too deep for you to do yourself and requires professional extraction.
use some Polysporin on popped whiteheads to prevent infection.
The 2% BHA solution exfoliates deep inside the pores, while the Intelliderm supplement has an Ayurvedic blend of herbs to cleanse the pores from within. I originally bought the supplement to help my hair grow faster - which it does - but was very surprised at the improved quality of my skin. I've been blemish/whitehead/blackhead free for months, and I have extremely acne prone skin, so that's a miracle for me.
I always get blackheads on my nose for some reason. I use those Biore strips...they work for me, but I've heard a lot of people say they don't work. You can look at the strip when you take it off & tell it works though.