Use this phrase when something is broken, causing problems, or difficult to understand:

We're having a little problem with one of our suppliers.

You can talk about a person this way also:

What's wrong? Are you having a problem with one of your coworkers?

"Having a problem with ___" is diifferent from "have a problem" because it's temporary. If you "have a problem with" someone, it means that you don't like them:

A: Do you have a problem with me?

B: Yes, as a matter of fact, I do. You're a lazy, selfish, jerk.