Sometimes there is no or little difference. However, there is a difference which shows up well in situations such as this... "My little boy tried to eat the carpet! Silly boy! You can't eat carpets. He chewed it a bit though." "My little boy tried eating the carpet. He really liked it. So I'll let him try the curtains tomorrow." Yes, the second one is a silly sentence. But if your little boy actually ate the carpet (to see what it tasted like) it's the second grammatical structure you need. Compare: He tried to open the door but could not. (It was locked, or stuck) He tried opening the door to see if it would help cool the room. (|He actually opened the door as an experiment) To try to do something... suggests you may not actually be able to do it. But you try. To try doing something... suggests you actually do it, possibly as an experiment. The difference almost disappears in some situations: I tried to read War and Peace but gave up. I tried reading War and Peace but gave up. Really, in this case, there is no difference. You started, didn't like it, so stopped. It's the 'but gave up' which makes the two sentences clear and very similar. You know what happened. You started, and at some point stopped. I always suggest looking at the whole context/paragraph. What is happening? Is this a failed attempt? Is this something someone actually did? I hope this help a little. It's a huge area of study... the 'to - / -ing' problem, I call it. (The TO versus ING problem) We get a similar problem with many verbs: for example, to stop to do something/to stop doing something. These have very different meanings, as I expect you know. Try to learn a few of these verbs at a time, try not to worry if you find them difficult. They are difficult! They are also easy once you get used to them! In summary, I suppose I could say, try to learn a few at a time (attempt it), and try learning a few at a time! (learn a few and see if that is a good way to do it).

This is the classic example of where the distinction between gerund and infinitive changes the meaning entirely. If you look in any good grammar book or on any good grammar site, the difference will be explained. If you 'try to do' something, it is difficult for you to do that thing, but you are attempting it. You try to climb a mountain, you try to fix your bike, you try to improve your English. These things are hard for you to do, but you attempt to do them. We don't know if you'll succeed or fail. 'Try doing' something does not have the same meaning. It means to experiment with a solution to solve a problem. Let's say that you want to buy a rare book. You are 'trying to find' this book. People might give you advice such as 'Try looking online' 'Try asking your friends for help' - these are not difficult things in themselves (it's easy to go online, it's easy to talk to your friends) but you do those as attempts to solve another problem.