How to offer someone help/support? Or: What would you like to hear when you need help but don’t dare ask?

I have a friend who’s going through a rough time in her life and I would like to offer her help, but I don’t know what to say. I know a lot of people don’t dare to ask for help because they’re afraid they’ll be turned down or that they’ll seem needy/weak, and I personally feel that way, too, even though I know it’s okay to ask. I just want my friend to know I’m there for her if she ever needs to talk or needs help with stuff that needs doing. But I’m at a loss as to what to say to her. My friend (we’re not really close anymore, more like acquaintances) has hinted that she doesn’t know who she could turn to, so I think she doesn’t know that I’d be there for her. I’m afraid that if I say it the wrong way, though, that she’ll feel like I’m talking down to her or not taking her seriously or that I think she’s weak or that there’s something broken about her. Also, I don’t want to come across as overbearing or make her feel like I demand her to accept my offer.

So, does anyone know how to offer someone help/support in a low-key way so it doesn’t come across as condescending or preachy, but still gets across that I’m serious and it’s okay to ask? If you’ve ever been in a situation like that, where you needed help but didn’t dare to ask: What could/should have someone else told you that you would’ve felt it’s okay to ask?

(Note: This is a repost of my original post from two days ago, which was deleted because my account was too young. I understand and accept that. I hope it’s okay for me to post this now.)