Of course, this may be the whole point of your story: the difficulty of communicating without a common language. It's a good theme to explore—though far from an easy one!
But if your story purposes lie elsewhere, you may have to find a simpler solution to the problem. Star Trek popularized the "universal translator," though it was hardly original to the series, and there are many variations on this device. In my own series, The Chaos Chronicles, the protagonist finds himself with tiny alien devices known as translator-stones embedded in his wrists. Among other functions, the stones enable him to communicate with various alien races that he encounters.
Another solution is to have aliens who have already mastered human languages, perhaps through previous contact, or perhaps through years of observing humanity (either by being among us, or by listening to our radio and television broadcasts from afar).
Still another approach is to give your aliens telepathy or other means of directly perceiving the thoughts of others. This removes technology from the equation altogether.
Whatever you decide, here are some things to think about in the area of human-alien communication:
Do your aliens use spoken or written words? This implies that translation is a possibility to be hoped for, perhaps requiring the discovery of the Rosetta Stone to make the crucial breakthrough. Or maybe no breakthrough will be made, and the languages will remain a barrier.
Do your aliens use poetry or metaphor to communicate? This implies some success in breaking the basic language barrier, but may leave your characters barriers of understanding to wrestle with still. Star Trek: The Next Generation once used this scenario to very interesting effect.
Do your aliens use another medium for their language? Possibilities include body language, pheremones and smells, music, emotional or empathic telepathy, verbal telepathy, and more.
Can you add to this list?
