Many pediatricians give six months as the usual time when babies start sitting up. In fact, the window is from four months to seven months, and the vast majority of babies can sit up by the time they are eight months old. Before sitting completely independently, you may see your baby supporting his back with his arms, though not all babies do this. With practice and preference, the time your baby will be able to sit up increases from a few seconds to much longer stretches of time.
Don't worry if your baby starts crawling before sitting up. This happens sometimes (my older child was like that) and is nothing to be concerned about. Of course, if you are concerned about delays or have noticed something unusual about your baby's muscle tone, do make sure to mention it at your next pediatrician's appointment or even make a separate appointment just for this purpose. Incidentally, sitting up is usually the ideal time to introduce the first solid foods to your baby. If you have an early sitter, you may want to hold off until he reaches six months, and late bloomers might still need solids. But as a rule, sitting up alone means being able to participate in mealtime.