When taking care of oily skin type, special attention should be paid to cleansing to prevent or minimize most of oily skin related problems. However do not over-cleanse or use too harsh products - this may strip your skin of oil and encourage oil glands to work overtime to make up for it.
Do not use bar soaps and hot water in attempt to dissolve and get rid of all of the oil on the skin surface and in the pores. This may result in dehydration of the skin and irritation. Use a mild cleanser with no addition of oil, waxes or any other lipid agent that can worsen the oily condition of the skin. Another good idea for oily skin is to use a cleanser with salicylic acid, a beta-hydroxy acid that reduces sebum (skin oil) production and will help you to combat break outs. Also it can be beneficial if your cleanser has antibacterial properties/ingredients. Oily skin prone to break outs will also benefit from a toner with antiseptic.
To counteract any dryness or dehydration that might result from deep cleansing of the oily skin use a light oil-free moisturizer. You may also try an anti-imperfection moisturizer but use it only if it is not too drying for your skin. Avoid any ingredients that can clog pores and aggravate acne such as cocoa butter, olive oil, corn oil, acetylated lanolin, butyl sterate and any other comedogenic ingredients (ingredients that tend to clog pores and cause acne).
If your moisturizer does not come with sun protection, use a sunscreen, preferably gel type, that has minimum SPF of 15.
The main recommendation for a diet would be to keep to a low-fat diet. Avoid oily foods: pork or foods cooked with too much oil. Also avoid highly seasoned foods. Read more here.