No rule says you must be clear or obvious when asking someone out. It can otherwise be awkward, especially with going the direct route of saying, "Do you want to go out on a date with me?"
Choosing an indirect but more casual alternative will nearly always be preferable.
We'll go over a variety of the best options on exactly how to ask someone out without actually saying it.
Before we start, remember the big picture: Whether or not they like you matters much more than the precise wording you use. No girl (or guy) will reject you solely from how you asked them out.
The best way to indirectly ask someone out is to treat them like a friend. When you suggest spending time together without making it seem like a traditional date, it helps take some of the pressure off. Text them for a few days, mention you're bored, and suggest spending time together.
One way to do this is to "test the waters" first.
Bring up something fun that might be going on. For example, let's say the fair is in town. Mention how you're interested in going and checking out the rides.
They may ask who's all going. You can just reply with:
"no one seems available :/"
At that point, the ball is in their court. Sometimes the girl (or guy) may need some extra nudging to get what you're hinting at. If they're actually interested in you, they'll usually pick up on it and say they're still willing to go.
If they haven't already agreed to go, you can add: "I'm still down if it's just us. I gotta check out that sketchy rollercoaster lol"
This example works since you suggest spending one-on-one time together without directly asking them out.
If he or she says no, you haven't been turned down as your intent was "only" on the fair. This strategy can apply to many scenarios, but it fits best with doing something unique.
Here are some other examples:
Most of the time, just mentioning your interest in something is enough. For instance, next time they text you wondering what you're doing, say something like "I'm looking into x" (with x being anything like gun range, an event, wine tasting, etc.).
If they want to go out with you, they'll usually direct the conversation forward by mentioning how they're interested in that too. Or, they'll mention how you both should check it out.
Check out What's Best: Asking a Girl Out Over Text or in Person? if you're unsure about advantages of either.
Inviting them out in a group with friends is a great way to indirectly ask them out. While it's not exactly a date, it can help further build your connection with them.
Spending more time together with building a connection will help make actually asking them out easier (and increase their odds of saying yes).
Where you invite them to doesn't matter as much, just make sure it's fun. It could be a party you're going to or a day trip to the beach that they could join. Your group of friends should ideally be a mix of guys and girls, though.
If you haven't talked to them much and are unsure when to suggest this, check out How Long to Talk to a Girl (before asking her out). It applies just as well to guys as it does to girls.
One clever way to suggest going on a date is to challenge them to a bet.
I did this once many years ago when I worked as a promoter. One job I had was in liquor stores giving out samples. A cute "tatted-up" girl happened to work there during my shift. It wasn't very busy, so I got to know her reasonably well over the 4 hours I was there.
We seemed to hit it off. At one point, she mentioned how she could "drink any guy under the table."
I saw that as a clear challenge. I said, "No chance," and got her number to "prove her wrong."
This unique situation won't apply to every scenario, but it's worth keeping in mind.
Another clever way is through a "creative circumstance."
For example, I did this once in high school. I told a girl I liked how I got 3 free tickets to a concert and suggested she should join me with a friend of hers. She said yes.
In reality, I made up the whole thing. I had some story about my sister giving me the tickets after finding out that she can't go anymore.
Unfortunately, I bailed and told them I couldn't end up getting the tickets. I can't remember the exact reason. It could have been nerves or maybe I didn't have enough money to buy 3 full-priced tickets. Sadly, no Gwen Stefani concert for me.
If you really don't want any chance of rejection, you should lean heavier on getting them to ask you on a date.
Ideally, It should be done through text, as it makes responding much easier (for both of you).
The best way to do this is to strongly just hint how you want to go out with them. One way is to bring up how you're bored and have nothing to do. With some luck, they'll ask you to go do something with them.
In this specific case, they could be genuinely busy so it's not always indicative of their interest in you.
You can also go a different angle by mentioning how you have nothing to do *this weekend,* which could help emphasize your availability.
Another option is to ask if they have any big plans this weekend. After they (hopefully) say they don't, they'll ask you the same. Mention how you don't have anything going on and are looking for something to do.
They should start suggesting ideas. If they don't, say "any ideas?"
Their ideas might not all relate to something you both can do. Just tell them the ideas are good so far and to keep them coming. Once they suggest something for you both, you can say how that idea: "seems pretty fun. but I don't have anyone to go with."
At that point (assuming they like you and are available), he or she will be the ones putting themselves out there. They'll ask you out by suggesting they're willing to come along. So, you'll have no chance of rejection.
Not being super being direct is smart.
It's also really best for both parties. If someone asked you this way and you weren't interested, it's much easier to reject them too. They should get the hint without dealing with the brutality of being turned down.
If you're still looking for ideas, another subtle option is working off of something they are interested in. If you know they like something (an artist, hobby, place, etc.), there's probably a way to work that in. Even better if it's a shared interest.
If you've succeeded with this or have experience doing it, let me know in the comments. Otherwise- good luck with "asking them out."