If you “give it a shot” it means that you “make a good effort”. It means that you “try at something”. It doesn’t mean you succeeded and it doesn’t mean you failed either, but you at least put in your best effort.
Here is an example you could say to your friends. “I am not a very good singer and I get nervous singing in front of other people, but I’m going to give it a shot today”.
Another example: “I’m not sure if that beautiful girl over there would be interested in me, but I’m going to at least give it a shot and go talk to her”.
In another context, you can “Give something else a shot”. It means that you try it and you give it a chance.
Here are 2 examples in this context:
“I’ve never heard of this restaurant before but it looks nice and I think we should give it a shot“. (That means you will eat at that restaurant and try the food)
“You guys have only been dating for 2 weeks. I don’t think you should break up yet just because of one small fight. Why don’t you give it another shot and see if you can work it out”