Let's just get this out of the way before we jump in. Asking someone else to promote your content is the equivalent of saying "You spent years building your audience by providing them with valuable content. Mind if I hitch a ride on your success instead of putting in the time to build my own audience?"
Asking someone else to do your work for you is looking for shortcuts and cutting corners. It is not a good idea and there are very few exceptions to that rule.
Having said that, if your situation is that exception and you feel it is appropriate to ask someone to share your content with their audience, then at least do it right.
Here are some good tips to follow:
Take a look at their last 20 posts and see if your request is relevant.
I am going to be very honest with you, this entire article came together this morning on the way to work. I got a random message from an acquaintance with a link. The link was to a service and she followed it with a request that read, and I quote, "Please share."
I was tempted to respond "No", but instead I tried to explain to her that this service is not even remotely relevant to my interests, the interests of my audience, or the kind of things I like to share. I explained to her that if I promoted every service people send me, my audience would lose interest, I would become irrelevant, and everyone would lose. She didn't get it.
If you have a new ballet school, I am happy for you, I truly am, but perhaps asking me to share it with tech-oriented readers isn't the best idea? Even if somehow, me sharing it would not cause me damage, would it even do anything for your ballet dance registrations? Did you think this through or are you just looking for some exposure that won't even move the needle?
If people follow me for tech updates, with a sprinkle of food photos, super car fantasies, and occasional family cuteness, would my post about your ballet school even draw engagement? That is a rhetorical question, but I will answer it anyway. No, it would do nothing and you'd get zero engagement and I would have done damage to my brand.
Not what you were going for, right?
Don't just share your link, include some context and explain why you think it is relevant.
These are the best. You send me a link without any accompanying text so I have to click through, see the content, read it, and then try to figure out why you are sending it. How about this approach? "Hey Hillel, I see you share the occasional car photo. I know this is no super car, but I am launching a new car business and I would be honored if you deemed it relevant enough to let your followers know about it."
By sending such a message, you accomplish a few things. First of all, you are being polite and considerate of my time, instead of putting me to work and expecting me to figure out what you need from me. Second of all, you answer the question "Why?" before I even get a chance to ask it. Always a good idea. Finally, you framed it in a way that you would appreciate the help as opposed to expecting me to do your work for you. It is all about the way you frame the request.
Before you reach out, take a look at their posts and make sure now is a good time.
Here is the thing with social media; people share things. So if I just shared a picture of me on a family outing, perhaps now is not the time to ask me to share your article about cloud infrastructure.
"You expect me to go into a person's social media and stalk them before emailing them?" Well, "Stalk" is a strong word but yes, if you are asking someone for help, it is your job to do research on their interests, their preferences, and yes, their activities. If you got lucky and the person posted recently that they're in a day of meetings or taking the day off, then you just saved yourself a negative response or no response at all.
If you are going to cut corners by asking others to promote your work, you better make sure you take their needs and behavior into account.