The main way into Chicago is along the Eisenhower Expressway (Rte 290), but if traffic is bad you can take I-355 or I-294 South to avoid things and take the Stevenson North (Rte 55), which lets you off a bit south of the Loop. The Stevenson is rarely as congested as the Eisenhower.
Once in the vicinity of downtown, you can go North-South either by the Kennedy Expressway (90/94), or by Lake Shore Drive - depending on your destination, of course.
Once you arrive at your destination, parking becomes the main concern. Many residential sections in the city enforce permit parking, which may allow you to park there without a permit during certain hours. There will be signs posted along these streets to tell you when you may park there without a permit. There is also metered parking along most non-residential streets, but a spot, particularly one near your destination, is often difficult to find. Some restaurants, clubs, and hotels will either have valet parking or a small parking lot, which may or may not be free to customers. Call ahead to check if a place has parking available. There are also many commercial parking structures in the downtown area, but these can be very expensive depending on what time of day you arrive and how long you stay. For destinations near the Loop, you may want to use the parking structures underneath Grant Park. These have many spaces and are relatively cheap ($14 for any stay under 12 hrs).