There's a cute person at the deli counter in the grocery store that I go to that gets really flustered whenever we interact. I catch them sneaking glances at me when we're not directly interacting so I think they think I'm cute, too. I think they're adorable and would like to ask them out but I've literally never done that before and have no idea how to go about it without seeming weird. I'm also ND and very socially awkward, please help 
I would recommend a slightly more subtle approach.
So they're pretty nervous and they get flustered around you, right? And a workplace might be an awkward place for them to say yes because of coworkers around but also they might feel pressured to say yes due to anxiety and being in a customer service role.
Then there's the whole thing about setting a time and place while a manager is probably only 60s away from breathing down their neck.
So I'd make a little note or card, something that can be put into their pocket easily, that says something fairly simple.
You might say something like "I think you're cute" or "I'd like to get to know you" to signal your interest and then something like "let's grab a coffee sometime" then write your phone number and sign off with your name.
Doesn't have to be much but this way is very low risk both for you and for them - it's very quick and discreet. It puts the ball in their court so if they want to take you up on the offer they can do so at their own pace. It means if they're not interested they don't have to reject you as a customer in public while they're at work. It also means there's no need to rush things trying to figure out what the next step is.
Just as general advice people tend to deal with it better if you let them know you're neurodivergent early on so they don't get mismatched expectations and so they don't misinterpret things. If I am giving someone the time of day or I'm working alongside them then I will drop mention of being autistic or ADHD in the conversation early on.
I think I'll go in with the intention of saying something as long as there's not a crowd around and have the note for backup. I've been psyching myself up all day.
I also just want to thank everyone here for being so supportive. I got really emotional reading everyone's responses
We're right behind you comrade :)
I wanted to tell you a little goofy story that maybe has a kernel of something useful within it:
Once upon a time I had this terrible pain in my balls. (Stay with me here lol.)
I hadn't done anything to cause it and due to the symptoms it was looking like everything was coming up as the most likely cause being testicular cancer. Oof.
The pain is really bad for days. I stop eating and barely drink enough. I'm kinda waddling when I have to walk.
Anyway I get to the doctor's office and get the referral for an ultrasound but he also sends me to the phlebotomist's office to get my blood drawn to see if there's any infection or whatever else. Oh and they want a urine sample too.
Cool cool.
Except they try to draw my blood and because my fluid intake has been barely anything, it's like trying to draw craft glue out of me. So I'm stuck there in the office, the paperwork is screaming "Homeboy's clearly got at least one (1) STI!!" and I hobbled in there like a 1970s B-movie ghoul from a horror film too. It's pretty obvious what's up (although it's really not an STI - not that this would be obvious to anyone looking in from the outside).
So I'm sitting in the chair for idk like an hour putting on a brave face and sipping water as best I could though the nausea and the pain to rehydrate myself.
They get the draw, at last. I've been chatting to this phlebotomist who has all my paperwork for the whole time. They seem really nice and they're kinda cute too.
I finally need to pee so I do all that and towards the end of filling out all the paperwork and stuff, I'm like (internally) "Fuck it - I could be dead in a year or less. They already have every indication that I'm carrying some sort of horrendous sex-organ plague. What's to lose? Might as well get a good story out of this, either one to regale the grandchildren with someday or one where I'll be dying from the chemo and the cancer as it takes me but at least I won't have this lingering over me as a regret..."
So I ask the phlebotomist if I can give them my number. And they say yes.
Now it's worth mentioning that I'm not especially dashing or brimming with rizz, although objectively I'm not suffering from any unusual deficit in those respects either.
So yeah. Sometimes you kinda need to gently nudge yourself and think - fuck it, the worst that could reasonably happen is that I'll experience some embarrassment and one day I'll look back on it and chuckle, regardless of how the chips will fall.
Anyway. Things didn't really work out between us. We were just too different and that's how it goes, so no ridiculous story to tell the grandchildren about how everything started. It's still a good story all the same though.
Oh and it turns out it was an epididymal cyst after all of that. So that's nice (?) too.
This is how I've been trying to get over this. Until now it's been a ridiculously high bar for me to make myself even the slightest bit vulnerable. The last person I really opened up to was a roommate that I talked to for hours from the first day she moved in. After probably 20 hours of relating stories and having a great time over the first couple of weeks of knowing each other, we were sitting on the couch late one night, there was a pause where we were just looking at each other, and something clicked in my brain and I made a move. It was the first time I'd ever done so. We had a brief FWB phase that never progressed into a relationship but we're still friends to this day. We never fought or anything, just realized we had different expectations. I think she knows more about me than anyone else in my life, lol.