Food - Fried foods and harsh fat or oil based foods are known to cause the excess sebum that leads to acne. For this reason a change in your diet is a good idea and will make a big difference if you currently eat these kinds of foods.
Water - Drinking enough good quality water is another important nutritional requirement for any natural acne cure and so making a good effort to drink 2 liters a day will help tremendously. The water will help flush out impurities from the system that otherwise often end up as acne.
Coffee and Tea - These two popular drinks are diuretics, which means they increase the rate of excretion of water and so can cause chronic dehydration. Limit yourself to one or two cups a day if you're a tea or coffee drinker, and increase your intake of water to make up for the extra water loss these drinks cause. Cutting out tea and coffee can often have profound effects on skin health.
Tea Tree Oil - This natural antiseptic and antifungal is good as a topical application for acne and has shown that it reduces inflammation externally. This helps the skin heal faster and acne won't be as inflamed or cystic when using this topical. Generally topicals aren't worth using and water will usually suffice, but tea tree oil is one of the better ones.
Vegetable Juices - Nutrient intake is an important factor in treating acne from the inside, and one of the best ways to get lots of quality nutrients is to drink vegetable juices. These can be found in supermarkets or you can make them yourself with a juicer and raw vegetables.
Good oils - Hormonal balancing can be attained with the use of fish oils and evening primrose oils. These healthy oils are full of essential fatty acids and one of their primary functions is to help balance hormones. Hormones are a primary cause of acne and so taking these oils can greatly help.
This has been a good summary of some of the more popular natural ways you can clear up your acne, although you may want a more comprehensive natural system.