There are two main types of dumbbell: fixed weight dumbbells and adjustable dumbbells.
For fixed weight dumbbells, a solid rule of thumb to follow is to aim to pay less than $3 per pound the dumbbell weighs. Usually, the closer you can get to paying $1 per pound, the better the deal, although this will depend on the quality of the weight.
Adjustable dumbbells are more complex, and will cost more as a result.
Spinlock sets, featuring central metal bars and interchangeable weight plates, will be the cheapest option, and you can sometimes pick up a 22lb pair for less than $50. That's why I was so surprised to see this Decathlon set for just $25 at Target.
More technical selectorized adjustable dumbbells, which have dial-controlled weight-changing mechanisms, will be the most expensive. Although in my opinion it's worth holding out for a trusted brand here, as I've found cheaper sets can have loose plates or a poor build quality.
The Bowflex SelectTech 552s are my favorites for training at home, and having kept tabs on their sale price over the last few years I'd say that if you can pick a pair up for anything close to $300-$350 then you're on to a winner.