A good thing to do is say it together with the word you want.
For example:
Which is easier to say, "thuh elephant" or "thee elephant"?
In this case it would be "thee elephant".
Which is easier to say, "thuh bike" or "thee bike"?
In this case it would be "thuh bike".
This might not work sometimes as it's easy to say both for some words. With time it will come naturally.