Oil cleansing and exfoliation. You'll never be fully rid of blackheads- even people with "perfect" skin have them- but you can lessen them. Exfoliation is the best way to do this. Personally, I prefer chemical exfoliation over mechanical, because scrubs and the like tend to make me itch more. Nip + Fab also makes a great cleanser with glycolic acid in it, I saw a lot of improvement when I used that.
You can also rub some kind of pure oil- I've used olive oil, coconut oil, and even sunflower oil for this- wherever you have blackheads and they'll pop right out. Oil attracts oil, after all.
To avoid double-posting, let me just gush about a sample I got yesterday at Sephora. I went to just look, I swear, but I ended up walking out with two of the UD vintage Vice lipsticks that were on sale for $11 (would've been three, but they were out of "Asphyxia"), and I used some of my points for a tiny pot of the
Sunday Riley Tidal enzyme water cream. And I can see why it costs $65 a pot! Oh my God, I can't stop touching my face, it feels so good!
It's pretty bad when you're willing to just eat cheap garbage so you can buy expensive skincare, right..?