Asking directly is the easiest thing - "Would you like to hang out together on Sunday afternoon?". Just remember that even if they decline that particular invitation, that doesn't necessarily mean that they are declining to move the relationship in that direction.
But here are some other options.
Say to them, "I'm thinking about doing {insert activity here} at {insert time here}". Like, "I'm thinking about tracking down some dinner." or "I'm thinking about going to see Brave on Sunday afternoon." (pause). That's all. Just mention it. Then listen closely. Their next statement will be your answer.
If they say, "that sounds like fun", or "I should too", then you can invite them to join you. If they poo-poo the idea, or respond with something like, "I saw it last week and I liked it", then you know that they're not interested in the event. If they totally ignore your hint, then you don't really know much. They might be declining your gambit, they might be uninterested, they might not have heard you or weren't paying attention, or they might be aspie and didn't recognize it as a hint. In that case, just let it go for the moment and try another gambit another time.
That's the best gambit that I know. There are others, but they aren't generally as effective.
For instance, there's, "we should do lunch". The problem with this one is that people rarely say "no". Instead, they say, "yes, we should", but they aren't sincere. So you have to sort of read the lies between the lines, or just assume that if they aren't willing to set a particular time and place, that they were only being polite and aren't really interested in developing your relationship in that direction at that time. "We should hang out some time" is basically similar.