Teaching your dog to go to the bathroom outside on a concrete patio isn't particularly difficult, but it requires a patient and consistent effort. In most cases, it should only take a few weeks, whether you're training a puppy or an older dog. Most importantly, remember that housebreaking your dog should revolve around positive reinforcement. Scolding or punishing your pet for accidents -- which are guaranteed to occur -- only makes her scared of you; it won't help train her and will likely inhibit the process.
Feed your dog at the same time every day so she'll become relatively consistent about when she needs to go out to relieve herself.
Take your dog outside hourly to give her the opportunity to go to the bathroom on the concrete patio. Puppies can hold their bladders and bowel movements for about one hour per month of age. As your dog gets older and better trained, you can go outside once every two hours for the remainder of the housebreaking process.
Put a leash on your dog and lead her to the exact place on your patio where you want her to go to the bathroom. Keep her there until she goes, or until you're sure she doesn't have to go.
Reward your dog when she relieves herself in the appropriate place. Pet her and enthusiastically tell her what a good job she did. Offer her a treat sometimes, but don't get carried away; remember, calories from treats add up quickly, especially for puppies and small breeds. Positively reinforce the behavior right away, on the spot, so your dog associates the reward with going to the bathroom in the right place.
Keep a close eye on your dog as much as possible during the housetraining period. If she starts circling, whining, sniffing the ground, scratching at a door or repeatedly leaving and returning to the room, there's a good chance she's trying to tell you she requires a trip out to the concrete patio.
Crate your dog or confine her to a small room when you can't watch her attentively while teaching her to be housebroken. She'll try her best not to soil a small area where she can't get away from her leavings. Keep confinement time to a minimum as much as possible, though.
Interrupt your dog if she starts going to the bathroom inside or in an inappropriate place outside. Just clap or tell her "no" in a firm voice. Don't make a lot of noise or yell; you're only trying to stop her, not scare her. Promptly lead her by leash to the right place on the patio and let her finish her business. Offer a reward.