Just as with any other destination, everything depends on where your hotel is, how much time you've allocated and what you are planning on seeing.  Let's take a look at a couple of scenarios below.  Each scenario assumes that you have three days and are only planning on seeing Disney.   

1.  You've decided to stay at a neighbor hotel, i.e., a non Disney resort that offers privileges to guests, but you also have a rental car.  If the resort is not within walking distance.  Your best bet is to utilize the Hotel/Motel shuttle for free (but only a few hotels have a private shuttle) if they offer one, or use ART. The other option is to take your car to the parks.  For a flat fee of $15 per day, you park your car and are then taken by tram (If you park at the Parking Structure) and dropped off outside of the main entrance by the World of Disney store.  From that point, you simply walk to the entrance of either Disneyland or California Adventure. Many hotels on Harbor across from the Disneyland Resort are within walking distance.

There is also the Anaheim Resort Transit system (ART) which operates from most of the hotels and throughout the Anaheim resort area.  Tickets can be purchased at the hotels. www.rideart.org

2.  You've decided to stay at one of the three Disney resort hotels and plan only to go to Disneyland and California Adventure.  Most folks don't need a rental car.   Disney does not offer any sort of tram service from the hotels, even though the walk from the Paradise Pier is the same distance as the Candy Cane Inn (who provides its own shuttle) and Howard Johnson's (part of the ART system).

Also, the local bus service is efficient and nice.  One popular question, where is the nearest grocery store to Disneyland.  It is a Food4Less (run by Kroger/Ralphs), one mile west of the DLR on Katella Avenue.  You can walk, or take the OCTA Route 50. www.octa.net

 3. You can take a bus down Katella to the nearby Amtrak/Metrorail station by Angel's Stadium. The Metrorail runs from San Clemente to Union Station in Los Angeles. From there you can transfer to local buses and the Red or Gold line to points in the city. The Amtrak train runs from San Diego to Santa Barbara with stops at Anaheim as well as Union Station. There's a surprising amount of public transportation around if you look for it.

If you are headed north to Union Station, the Fullerton Train Station is a great option, about the same distance from Disneyland as the Anaheim Station, and it is easier to get to than the Anaheim Station by public bus (OCTA Route 43 north)

For easy shopping, you can take Route 43, that runs up and down Harbor North to Orangethorpe.  This location has a LOT of choices, including a Super Walmart, Target, a Disney Outlet store, Costco, Sprouts grocery store, plus popular restuarants including In-n-Out Burger (a Southern California classic).