As the closest major resort island to Athens, Mykonos gets large crowds from April through October. This is a party island and is popular with visitors from all over Europe and the rest of the world. Those looking for a low-key experience might be better off elsewhere.
Along with Santorini, Mykonos is considered one of the more expensive Greek Islands. This primarily means that budget offerings are harder to find, although they are still there for those who go out of their way. The main beach and nightlife areas will all feel relatively expensive, at least for Greece.
Hotels and hostels in Mykonos run the gamut in prices, although the cheaper places are probably of low quality or with poor locations. Visiting outside of the busy July and August season will obviously save you money and keep you out of the insanity.
The few attractions on Mykonos are fairly cheap, although most people come here to sit on the beach during the day and drink at night. Renting a chair and umbrella for the day can be an inexpensive way to rest up for the party later that night.