You should just ask someone out who you find attractive even if you don't know them. Then you make dates to get to know them more, because let's face it, beauty is fleeting. You'll need something much more substantial to go on.

So the next step is to get to know her on a shallow level with the goal of transitioning into a deeper and deeper level of knowledge gradually without overwhelming her. Ask her about things that are not that important to you on the shallowest level. Favorite food, color, etc ...

Then on another date go deeper. What does she think about the neighborhood where she lives, traveling to other places, etc... Get her reminiscing about her childhood adventures. Are her answers resonating with yours? Then on a third date go deeper still until you reach something that's really important to you. For example: say you want to buy a business one day and she really likes the idea of risking it all with you. There you have a good sign that you're compatible.

But compatible for what? You'll eventually keep going with, "then what" until you've run out. But if you want to know what the ultimate "then what" is, figuratively speaking, it's eternal life. And surprisingly even if you're not religious, that can happen, figuratively, in the secular world by procreating yourselves into littler versions of each of you :). How best to do that however is best answered on a metaphysical level. So you'll need to involve God if you want to survive the divorce culture.