Gentle, water-soluble cleansers (and avoiding bar soap). The ingredients that keep soap in its bar form can clog pores, and irritation can cause skin cells to flake off before they're ready and accumulate in the pore.
There are lots of gentle cleansers to consider, ranging from Alpha Hydrox, Aveeno, Cetaphil, and Neutrogena to Paula's Choice. It's actually getting more and more difficult to find a cleanser that isn't gentle. Someone with dry skin would want to use a slightly more moisturizing cleanser—but be careful: cleansers that are too emollient leave a greasy film on the skin and that can cause further problems.
Gentle exfoliants that can both remove the excess skin cells on the surface of the face (so they don't build up in the pore) and exfoliate inside the pore (to improve the shape of the pore, allowing a more even flow of oil through it). Keep in mind that the pore itself is lined with skin cells that can build up, creating a narrowed shape that doesn't allow for natural oil flow. But don't get carried away with this step. Overdoing it (removing too many skin cells) can cause problems and hurt skin. Exfoliation is essential for both dry and oily skin to eliminate blackheads or whiteheads.
Again, someone with dry skin will want an exfoliant that has a more moisturizing base.
The best option for a good exfoliant is a 1% or 2% BHA gel, liquid, or lotion. There are still only limited options for this one, including Paula's Choice 1% or 2% Beta Hydroxy Acid, Serious Skin Care Clarifying Treatment with 2% Salicylic Acid, and Neutrogena Clear Pore Treatment with 2% Salicylic Acid. If you cannot use a beta hydroxy acid you might want to try an alpha hydroxy acid.
By the way, topical disinfectants such as benzoyl peroxide or topical antibiotics available by prescription do not help in the treatment of blackheads and milia because there is no bacterial involvement related to these conditions.
Absorbing excess oil. This step is for those with oily skin and is not necessary for those with whiteheads and dry skin, because with dry skin the problem isn’t excess oil, it's trapped oil. For those with oily skin, you all know I prefer milk of magnesia (a few companies, including mine, have cosmetic versions of this step). Clay masks are an option. Though not my favorite, some women do like these, and as long as they don't contain other irritants, they can have a positive effect in absorbing oil.
Effective but optional considerations for all skin types are Retin-A, Renova, or Differin. These can be used on their own or with a BHA product. Research has definitely established that Retin-A, Renova, and Differin have positive effects on how pores function, and these products should be a consideration for very stubborn cases or when blackheads are accompanied by breakouts.
For those with oily-skin troubles, hormone blockers or certain low-dose birth-control pills which reduce the hormone levels that create the excess oil may be an option. And, when all else fails, Accutane can be a consideration. Though many doctors are reluctant to prescribe Accutane for "merely" oily skin and blackheads, for those with that kind of persistent skin problem, it does not feel like a "mere" problem in the least and Accutane can be a cure.
For all skin types, AHA peels, microdermabrasion, and laser resurfacing can have some impact on the appearance of blackheads and milia; however, they don't improve pore functioning—rather, they temporarily get rid of the surface problem, making the skin look better.