Wash and prep fruit. For strawberries, hull or cut off tops; then halve or quarter. For peaches, apricots, and mangoes, peel and pit fruit, then cut into chunks. Leave small berries whole--(blackberries, raspberries, blueberries).
Put fruit into a blender or food processor and process until fruit is smooth or to whatever level of smoothness/chunkiness that you prefer. Note: for blackberries, raspberries, or blueberries, you may want to strain them through a fine mesh strainer or cheese cloth to catch the seeds before proceeding with step #3.
Pour puree into an appropriate size sauce pot and add sugar. Stir to mix the fruit puree and sugar.
Over medium or medium-low heat, bring the fruit mixture to a simmer and cook for 5-10 minutes, stirring frequently so that the fruit will not stick to the bottom of the pan. Do not boil because the sauce will burn quite easily and will also splatter out of the pot.
If you find that the sauce is thicker than you'd like, simply thin it a little with either water or a fruit juice of choice such as apple, pear, orange juice. Remember that the sauce thickens as it cools. If by chance, however, you find that the sauce is too thin after it cools, simply reheat and allow sauce to reduce.
At the end of the cooking time, turn off heat and stir in flavorings or extracts.