Ask up front and be polite. If they don't allow dogs, you can politely ask if there is anything you could do (pay a larger pet deposit, show proof of training, etc). If they say no, just move on. You may have better luck if you look at small house rentals rather than apartments.

Please do NOT become one of those people who abuses the emotional support animal rules to force a dog into a building that doesn't allow them. Respect that owners and other renters alike may prefer not to have a dog in their building either for reasons of allergies or not wanting to listen to a dog howl all day long.