There a number of signs that you should watch out for that can indicate that your dog has fleas including the following:
1. Excessive scratching. You may notice that your dog is scratching, licking or chewing on particular areas of their body more than usual. They may also shake their head a lot or scratch at their ears. 
2. Red bumps. Inspect your dog's skin for any red bumps. Common places where these bumps may occur include on the stomach, beneath the legs, on the rump or at the base of the tail.
3. Hair loss. If a dog continually scratches or chews at a particular area, they may start to experience hair loss in that area. If the fleas are not treated, the skin can even become infected or develop crusty lesions.
4. Tiny black flecks that appear on a flea comb. Buy a flea comb and comb your dog's fur. Even if no fleas appear on the comb, they may still be infested if you spot small black flecks on the comb. These black, pepper-like flecks are commonly called "flea dirt", but are actually flea feces. To tell for sure whether they are regular dirt or flea dirt, place them on a damp paper towel. If they turn reddish-brown, then they are flea feces, which means that your dog has fleas.  You can also have your dog stand over a white piece of paper and comb them. Again, little black flecks of flea feces may fall off of them onto the paper.
5. Visuals signs of fleas. The most obvious sign that your dog has fleas is if you can actually see them in their fur. Try slowly petting them backwards and watching the area where the fur is lifted. You may see fleas scrambling to hide when they are suddenly exposed as the fur is pulled back. Again, you can also use the flea comb. Typically any fleas that are in the area where you are combing will become trapped between the teeth of the comb. Fleas often hide behind the ears, under the chin or above the base of the tail, so you may want to start by combing these areas. Keep a bowl of soapy water on hand while you comb that you can put the fleas in once you comb them out of their fur.
6. Signs of fleas in the environment. Fleas don't just stay on your dog. They also infest the surrounding area. Check your dog's bedding for signs of fleas such as black specks. You can also set up a trap for fleas by placing a dish of soapy water underneath a nightlight that is plugged into an outlet. As the fleas jump toward the heat of the light, they will fall into the dish of water and drown. Leaving the dish of water out overnight can usually help you determine whether or not your house, and thus your dog, has fleas.
If your dog is scratching but you don't see any signs of fleas, you still may want to take them to the vet to have them checked out. Sometimes even a single flea bite can trigger an allergic reaction in dogs.
Here's a video that gives an outline of all of the steps that you can take to tell whether or not your dog has fleas: