Petco and PetSmart sell a cleaner that gets rid of the stains and odor called "Natures Miracle".
The bacteria-based formula produces enzymes when it comes in contact with bio-based messes including severe urine, diarrhea, vomit and blood. The Stain and Odor Eliminator is safe to use on carpets, hard floors, furniture, fabrics and more, when used as directed, and leaves you with a light fresh scent.
On concrete, carpet, hardwood?
The enzymatic cleaner mentioned above is what has worked best for us. Good luck!
It will help to have a dehumidifier to keep things dryer in the basement. You don't mention what you have to clean. Floors--what kind? Furniture-what material? Walls? How long have you had an issue with dog urine in the basement--that's a factor too! Phew! I hate dog and cat urine smell in the basement! Give us some more information so we can be more specific for your situation!
Sweep up any dust or dirt. Enzyme products often work. I have used PineSol and a scrub brush on unsealed concrete.