How do I know if my dog is constipated?

After two days of no output, I'd suggest calling the vet, to ensure there isn't anything serious (like an internal blockage). He may need medical attention.

If only a day had gone by without a bowel movement, I'd try moderate to long walks to naturally create the urge for the dog to relieve himself, give a spoonful of pure pumpkin (not pumpkin mix, no spices added), monitor if water intake is normal. (A dog may refuse or limit water if has painful UTI/stones and that lessened hydration could cause constipation.)