Try + -ing: to do something in order to see what happens, to see if it can help you to succeed in doing something, eg. "She didn't want to work for me any more, so I tried giving her more money; I hoped that this would make her change her mind about leaving", "If the baby doesn't like his cream, try putting some sugar in it". In the above examples, we do something as an experiment, that is to see if in this way we can get what we want. We don't have to make an effort.
Try + infinitive: to make an effort in order to get what you want: "I tried to lift the box but I couldn't because it was too heavy", "The prisoner tried to escape by filing the window bars", "We must try to attract new customers".
I hope you can see the difference. If not, try reading my explanations again. If you still don't get it, I'll try writing some more examples for you later on. I'll try to write better examples next time, but please try to understand that it's not always easy to explain everything.
So, here's a little test. Why don't you try doing it and see if you get your answers right. All you have to do is try to find the correct form (-ing or infinitive) to use:
-It was too hot in the room, so I tried (open) the window hoping that cooler air from outside could make things better.
-The old window was stuck and it wouldn't move no matter how hard I tried (open) it.
-They're trying (get) a loan from the bank, but their bad credit doesn't leave them much hope.
-If you want your girlfriend to come back, try (invite) her to dinner at a nice restaurant?