For the most part, parking at DU is an absolute mess. Street parking is often taken over by the ongoing construction on campus, and non-student residents in neighboring areas often complain to administration that students fill the only available parking in front of their houses.
If you plan on driving to class every day, or want to keep your car on campus, buy a parking permit. Permits can get fairly expensive, especially for restricted lots, but they're well worth it. In fact, the cost of a permit will probably pay itself back in the end, as you won't have to pay parking tickets from DU or the City and County of Denver. Both parking authorities are diligent about ticketing on a daily basis. Students who run out of class to move their cars from one-hour parking are often filled with dismay to see they're one second too late, and must watch as the parking patrol writes them a ticket. Pleading and begging to the officer on duty usually falls on deaf ears. If you buy a restricted permit, the lots are spacious and strategically placed throughout campus. Many feature underground or otherwise covered parking. General lots are fewer and tend to fill up more quickly. Some students use the general lots, particularly the large one next door to Halls and across the street from Towers, as car storage units if they don't drive very much, but wish to keep their cars nearby.