Blackheads are not dirt, they are the result of the natural oils on your face being oxidised.
Here are some natural remedies you could try to get rid of blackheads.
1. Wet a flannel in hot water *be careful it's not too hot* and hold it on your nose until it loses it's heat. This will open up your pores, making it easier to get rid of what's in the blackheads. Sounds weird but try putting PVA glue on your nose. Give it 10 minutes to go clear and dry then peel it off, the results will be on the peeled-off glue.
2. Heat up some honey and apply it to your nose (or wherever the blackheads are) leave this to work it's magic for 15 minutes and then wash it off. *Make sure the honey is not too hot as honey can burn you*
3. Lemon or Lime juice (salt optional) left on the face for 15 minutes.
4. Scrub toothpaste on your nose each morning and night with an old toothbrush.
5. Make up a mixture made up of 1/2 teaspoon of salt & 1 teaspoon of salt. Wet your face with hot water to open up your pores. Apply the mixture to the effected area, rubbing it in a little bit. Leave it to work for 5 minutes and wash off. Only do this 2/3 times per week as it can dry out the areas of your face that you've applied it to. If so, add some moisturiser.
As far as I know, there isn't much anyone can do to prevent blackheads (or spots). Just wash your face every morning and every night with soap and hot water, use any special face washes etc you have. If you're a girl, clean your make-up brushes and sponges regularly as these can be the perfect breeding ground for bacteria. Just wash them in baby shampoo (e.g. Johnson's baby shampoo) and leave them to dry naturally.
I hope this helps