I get it. It's embarrassing to tell people you're broke, and you can't afford to do all the things they might like to do. I've been there.
This may sound like a cliche, but one that's nevertheless true: Real friends will want to be with you no matter what your circumstances. Most of the time all they want is your company and your conversation.
Still, everyone must eat, right? So find ways to spend time with them doing the things that you would otherwise do. Invite them to go grocery shopping with you. Invite them over for coffee (or whatever you drink) on weekend mornings. Invite them over to make dinner together some evening.
Or what about activities you already do, like exercise and entertainment? Invite them to go on a power walk in the park. Invite them to watch a TV show you like, or a movie that's on TV. Invite them to help you work in your garden, if you have one and you like that kind of thing.
Also, you'd be surprised how many free events there might be in your area. Many communities and venues offer live concerts for free, or opportunities to dance, or art shows, or live theater, or movies in the park -- they list goes on and on. I live in a larger city, but even so I know of at least ten to twenty bars that have live bands where there is no cover charge if you get there early enough (naturally you are expected to drink, but it's not required).
Essentially, don't worry about whether the activity you invite them to is something they'll enjoy. The point is that you enjoy it, and if they like you, they might have a good time because you are having a good time.
And hey, you know you're not going to stay broke forever. Finding good people to hang out with -- true friends, who aren't just with you as long as they're being externally entertained -- well, that's something you just can't buy.
(Edit) To answer the specific question of what to say if she invites you to do things that cost money: Politely decline, saying that you would love to but you need to save money. Focus on your need to pay for important expenses, not what you think of as your overall lack of money.
Thanks for the invitation Mary, but I can't go out drinking with you tonight. I'm trying to put together enough to take care of this problem I have with my teeth.
If she says that she'll pay for you, you can accept but limit the degree of largess. You can also insist on repaying her with some kind of return gifts.
Okay, I'll go -- but only two drinks? Any more than that and it'll feel weird. Also you have to let me repay you somehow. How about you come over to my place Thursday evening and I'll cook us dinner?