Here are the steps to buy a house:
1. Tap on any OPEN HOUSE
2. Tap "ENTER" in the "PREVIEW HOUSE" pop-up
3. Tap "HOUSE DETAILS" once you're at the open house, then tap "BUY"!

You can use the OPEN HOUSE navigation at the bottom left corner to easily locate OPEN HOUSEs in a city. Remember, you can only renovate one house in each city you've unlocked and you can keep track of all of them through the WORLD MAP!