The only way is to carefully squeeze them out, I believe. Use tissue so you don't scar your face. "Steam" your face first so your pores are more open. They don't go away on their own, sadly.
You can't get rid of them as such because it is dirt in open pores - which won't close again unfortunately.
I had a microdermabrasion facial a couple of weeks ago (it's an intense exfoliation) and that cleared out loads of blackheads. I'll go for another one in a couple of weeks.
Repeated sauna can help clear them out, and can help close the pores after. Heavy exercise where you get red-faced and sweating can clear them out too and makes your skin look younger for a couple of days.
I heard somewhere that you can have this 'face vacuum' thing!!! I don't know if its true. Its where they steam your face and open the pores and then do this vacuum thing and suck out the black heads! I am gonna have to find out now. :o)
I've answered this before, successfully, get a Biro pen, take out the ink tube, then place the thin end of the empty case over the Blackhead, press in, pull out, no more Blackhead or root, this really works, try it.
You can buy Biore facial strips from Boots. You wet them, put them where the blackheads are, leave them to dry and then peel them off. They are really good.x