To "give someone a hard time about ___" means to tease them, joke with them, or yell at them about something. You usually use this phrase when you're talking to your friends and doing things like:

• asking them not to give you a hard time
• telling a story about how someone gave you a hard time

For example, if your sister is complaining because you didn't come to a party that she planned, you can say this to her:

Come on! Why do you have to give me a hard time about that? I told you: I had to work.

Here's an example where you're telling a story:

When I was growing up, the other kids used to give me a hard time because of my weight. But I just tried to ignore them.