Bearded dragons are known not to be aggressive reptiles; you are generally able to hold them and interact with them without fear that they will try and hurt you. Bearded dragons are one of the most friendly sociable reptiles, but you must remember that they are not furry and cuddly like cats and dogs. They are also smaller and more fragile, so care must be taken when interacting with your pet dragon.
Unlike human teeth that are separate and individual, the bearded dragon's jawbone is all one piece, and the individual teeth that you can see are part of the structure of their lower skull. They use their jaw as we do to chew their food and kill their prey when they need to, they have a powerful bite as is required to bite and chew some of the more robust parts of their diet. Their strong jaws mean that if a bearded dragon bites you, then it can hurt. How much it can hurt, does depend on the size of the dragon, smaller dragon's bites may only feel like a pinch and not draw blood, whereas a larger dragon's bites can cause a wound and be considerably painful.
They do, of course, also have their nails, but they don't use them to scratch you on purpose. However, if their nails are allowed to get long, then you can be scratched accidentally, and this has the potential to cause a wound. Their nails, just like ours, can collect bacteria from whatever they have been in contact with, so you should disinfect any injury caused by their nails.
Aside from their bite and their nails, they don't have any other way to cause any harm to us. Even though their bites hurt, dragons are very docile, gentle creatures that do not seem to want to bite us, they only do so as a defensive reaction, and even then it only seems to be a last resort, so it is unlikely they will bite you unless you mishandle them. So be sure to try and be careful when handling your dragon, so you don't cause them any distress, be gentle and aware of how you are picking them up and how you are holding them. If you are to get bitten and it causes a wound, simply disinfect and treat like you would any other would with a band-aid or whatever you need, seek medical advice if necessary. Their bite does contain a kind of mild venom, but it will not cause you any harm whatsoever.