If you want to get through your spring cleaning while retaining your sanity, it's a good idea to come up with a plan. You'll probably find it's best to work one room at a time, rather than bopping back and forth between rooms. There's a sense of accomplishment that will come from completing a room and closing the door, and you're going to need to summon that feeling somewhere around the middle of your project.
An important rule of thumb is to work from top to bottom in each room. If not, that pesky thing called gravity is going to make you do double duty on the dusting and washing. Walls, in particular, get pretty grimy from day to day, so they're a great place to start in each room. No shortcuts! Take down curtains and art; they'll need to be cleaned, too. Use your vacuum attachment to remove dust from windowsills and baseboards, then get out your mops and sponges and start washing. Use a toothbrush for dirty crevices, and be sure to change your water frequently so you're not adding grime instead of removing it. Work around the room in sections, but be sure to work all of each section at once so you don't have to backtrack.