There are said to be 1,000 curves along the Amalfi Coast, and there are probably around that number of places to stay too; from little pensione to the ritziest of five-star palazzi. For that reason, it's still possible to get a real bargain but you'll have to do your research and, needless to say, if you're prepared to come off season you'll knock even more off the price.
So, my tip would be 'flexibility':
Location: you might want to stay in Amalfi, but don't rule out nearby Furore or Minori; the little towns around Amalfi are usually served by a bus service that is cheap, regular and relatively quick. Where there is no bus service, many hotels and even a few B&Bs offer a shuttle service or, in the case of Vincenzo of Agriturismo Villa Maria, will simply drop you down to the town centre whenever you want (within reason) so you get the benefit of cheaper accommodation, a bit of peace and quiet and you're still close enough to the action.
Time of year: you'll pay a premium for visiting in high season so consider a trip at the beginning or end of the season; in March and October you will often have lovely, warm weather and miss the crowds.
Book ahead: once you've decided where and when, book it. In spite of the fact that there is a wealth of accommodation available, the Amalfi Coast isn't getting any less popular and if you want to be sure of getting your dream holiday, book in advance.