I've always preferred giving out my number instead of asking for hers.
Why?
Because it's less of a needy request than "Can I have your number?"
Also, it gives them the power to reach out if you had cold approached them. It's better to not put them on the spot for giving that info (to a complete stranger).
We'll go over giving your number:
Through social media to a girl.
To someone through your work.
To a girl a girl at a club
To a girl from your school.
Lastly, we'll also touch on using excuses to give them your number (which makes the process way easier).
There are many different options to use based on who she is and how you know her. If I didn't list your situation, let me know in the comments.
This is going to be one of the more challenging options.
You'll have to push through any worries about coming across as a creep.
It's the beauty of cold approach, though. Meeting new women anywhere at any time is an invaluable skill.
The main thing to remember is to be genuine and make the interaction brief. Maybe wait a moment for the line at the cashier to dissipate (if possible).
The important part of actually having a dialogue is for her to get a read on you.
You don't need to chat a lot, either. Even a conversation lasting one or two dozen seconds can be enough for her to screen most men.
Not doing so could make or break your success.
However, giving your number on a piece of paper is better than nothing.
First, I would probably use the back of a business card if I were to do this.
But any small piece of paper would work.
Along with writing my number, I would add something along the lines of:
"Thought you seemed cool 🙂 here's my # if you'd ever want to chat"
The creative part is how you give it to her.
If this is a retail clerk, you can hand it off as an exchange when you grab your receipt.
Otherwise, I would walk towards them, smile, and say "I have something for you" before handing it off.
One of the best/easiest ways is to just slide into her DMs.
Begin by adding her and starting a conversation.
If she's interested in you, she'll keep chatting. At some point (after maybe a couple weeks), just drop your number:
"hey it's a bit easier to chat over the phone. Here's my number xxx-xxx-xxxx"
Ideally, you should gauge interest in her first. It's awkward if you ask her directly and then get rejected.
There's no rush if you see her everyday.
So make sure you're regularly talking. Start chatting if you don't already know her (even if it's just small talk). If your job has them, go to any work events (assuming she goes to them).
It will help you get to know her better in a social environment where people are (probably) drinking.
When it's time to ask, it'll be super simple natural:
"hey I don't think you have my number yet"
I have a complete breakdown for this in How to ask a coworker out.
Generally, you'll want to have rizzed her up or even danced with her first.
When it's time, you can keep it very simple.
As it's likely loud, go up near her ear and say:
"Let me give you my number"
If it's super loud, you could literally type it out on a note and show her your phone:
"Here's my number xxx-xxx-xxxx"
However, clubs are typically best to make the move that same night. They may not remember you that well the following day.
Like at work, giving a girl your # from school is best done gradually.
Get to know her first.
Let's say she's someone in your class. You can give her your number for the sake of "learning."
This could mean asking to join your Whatsapp group for the project you have.
Or, maybe it's to collaborate or help each other on an assignment.
Ideally, you would already have a group chat going with others (so it's more natural). Not a big deal if you don't, though.
As explained in How to ask a girl to hook up, going the indirect route makes things much easier.
This is because you somewhat make it seem like you're getting (or giving) a number for a different reason.
The first example has already been mentioned. You give a girl from your class your number for the excuse of collaborating with school work.
Depending on your situation...
You may need to be creative with this.
It's much easier if you're already chatting with her.
Think about what you've talked about in the past:
Express your own interest in what's relevant to her. Mention that you have some questions, and then give her your digits.
Maybe she's in your extended social circle:
This is actually a bit of a controversial topic.
Guys generally think they should be the ones asking for her phone number.
Yet women prefer men offer theirs.
I definitely "get that" for men to some degree.
You're relying on her to send that first message. That may have lower odds than her just responding to a message you sent.
On the other hand, giving her yours is a move that shows confidence. There's no pressure on her, which is especially important for cold approach (where you're a complete stranger).
Giving yours just seems much more casual, which helps make it easier.
In the end, if they like you, it likely won't make a difference if you give your number or ask for theirs.
The biggest challenge is actually following through with it