First, are we talking about STBXW or some new girl? Because my response would be different, depending. If it's someone new and she tells you about a problem but does not ask for help per se, I would say something like:
- that's really awful! - ask her questions about the situation to get more information if she seems like she wants to talk - ask: "is there anything I can do? I'm always here to listen, but please let me know if you want my help or input--" and depending on her response, go from there. If she says "I don't know what I need right now" then give her a hug if appropriate, or touch her on the arm and say "I'm always here- if you think of anything I can do to help, please let me know". And leave it.
Regardless of which way it goes, don't go too far in either direction- don't swoop in like superman the minute you get the green light- proceed with caution in little steps and take your cue from her. You can always ask in the middle of giving your input or some kind of concrete action: "is this helpful to you? If not, please let me know if you need something different." It's always ok to ask and that is how you will get the most useful info. We can tell you what WE want, but it's not a one size fits all. And don't act too intimately for the relationship level, or you will scare them off- i.e., if you're just getting to know someone, don't offer to pay for their car to get fixed or something- that's too much. But you can offer her a lift or a ride to the repair shop, etc. By the same token, don't back off so far b/c of your past experience that you appear uninterested and just grunt or say "Hmmmmmmm....." in response or something when she opens up.
If it's someone new and she tells you about a problem but does not ask for help per se, I would say something like: 
