Milan is a year-round destination, but some months are better than others. May and September are best as the weather's likely to be good but it won't be too crowded. July and August are the Italian tourist high season, so the city is busy but buzzy; from mid-June to mid-August it tends to be hot and humid. October is the rainiest month, and from November to February it somehow manages to be cold but humid! Avoid the Fashion and Design Weeks (1 in Feb-March and 1 in Sept-Oct) as everything gets booked up and the city becomes very hectic.
Milan's public transport (ATM for central Milan, SITAM for greater Milan) includes a metro system, regular buses, 24hr trolleybuses and trams. It's cheap - a single, multi-transport ticket is €1 to anywhere in the city, while a 1-day pass is around €3 and a 2-day pass around €5.
Milan now has a bike-sharing scheme. You must register first, buying a temporary BikeMi subscription at one of many ATM information points.
Driving is not recommended - leave your car at one of the commuter car parks off the city's ringroad, then take the metro into town from a nearby station. There's a congestion charge of €2-10 per weekday, a one-way system, and parking is difficult and expensive.