Direct From Manufacturer
Ordering direct from the manufacturer is the easiest method. Parts are always in stock, and you can easily find the manufacturer's contact information in your dishwasher's user manual. Part numbers are in the manual as well, making it easy to order the replacement rack right from home. Most manufacturer's also have a website, allowing you to shop for parts and make the purchase online, at the click of a button. Shipping typically takes under a week, and most times an overnight shipping option is available, getting you the replacement rack within a day or two.
Appliance Parts Stores
While appliance stores typically look to sell you a new appliance instead of repairing the one you have, there are stores that specialize strictly in the sale of appliance parts. Dishwashers are common, so most stores will carry replacement racks for the major brands. If they don't, they will have a catalog that allows you to select the color and model of the rack you need. If ordering from the catalog, the rack will be shipped either to the store location for your pick-up, or directly to your home address.
Some online retailers also specialize in the sale of appliance replacement parts. Stores like APWagner.com allow you to search for dishwasher replacement parts by inputting any combination of brand, model number, part number, or description. They also offer some standard-sized products that will fit a number of dishwasher makes and models, so if looking for a generic rack at a discount price, simply make sure the generic rack is compatible with your brand of dishwasher (compatibility guides are listed with each item).