Robin got it right, any extra oil, grease, dirt, or other foreign matter will aggravate pimples. I had a moderate acne problem through most of my teenage years, and here are some things I learned:
Keep affected areas, especially face, as clean as possible. Do this by:
a. scrubbing them well with soap daily; and
b. thoroughly cleansing with rubbing alcohol subsequent to soapy scrub.
Avoid rubbing affected areas throughout the day; the oils and trace soils from your hands may seem negligible, but they contribute a great deal to the problem.
Warm pimples pop best (what? Do you think this is gross? Well, it's not, it's life.). Right after showers are the perfect time, and be sure to follow up with rubbing alcohol.
The rubbing alcohol helps prevent new pimples and gets rid of some small ones, but doesn't touch the big ones. I tried Acne-Free Severe for a while, and although it worked fine, it irritated my skin, which would get dry, itchy, and sometimes experienced a sensation approaching tingling. I hardly used it after a while because of that. Believing that the treatment was too severe, I tried Neutrogena Daily Scrub, along with their On the Spot treatment. It worked well for me without the dryness.
Edit: As I have mentioned, cleanliness seems to affect acne a great deal, and triggers eruptions, but it should be understood that the dirt is not what causes acne . I highly recommend reading the page at this link. Among other things, it states that acne isn't caused by dirt, and gives a professional assessment of a few related factors, as well as mentioning some possible courses of treatment. For severe cases, even some antibiotics can be prescribed by physicians. (But if it's not absolutely necessary, this course of treatment should be avoided, of course. :)
Also see this page, from which I quote, "Acne is not caused by lack of cleanliness. Although not cleaning the affected or prone areas leads to accumulation of sebum and dirt in susceptible persons raising risk of acne." (Sebum and dirt cause pore blockage, resulting in acne breakouts.)
Also see this page. Some of the content seems to contradict other sources, specifically, claiming that fatty foods make acne worse. While other sources refute this idea, this page points out the increased likelihood that your skin will become greasy from contact with such foods. (I would note that other health effects of avoiding fats are somewhat controversial, but since this is well beyond the realm of this discussion, I'll spare you from my viewpoint on the subject this time.)