I thought this thread was going to be about verbs like 出し抜く, which uses two different verbs to mean something quite different from the original meanings.
Where exactly are you having these problems? By the examples you've given, it seems that it's when you're trying to create Japanese constructions based on English. For example, the verb 'can' is used to form English potential, but Japanese creates the potential by conjugating the verb differently, so combined verbs aren't necessary in this case. The concept of trying is expressed in more than one way in Japanese, neither of which reflect the English.
If you're working through the lessons on here, or a textbook, then carry on with it and you will cover all of these points eventually. Getting a grammar dictionary might be a good idea if you have a good bearing with grammar and just need to look up new points. For the latter, I'd recommend A Dictionary of Basic Japanese Grammar/A Dictionary of Intermediate Japanese Grammar by Seiichi Makino.
Of course, if you have any problems on anything in particular, then feel free to post on here and somebody will no doubt help you.