So, this is partly from a physics lesson at school, and partly from documentaries and my own knowledge, I will attempt to illustrate in a simple way, how the universe can be infinite, yet be expanding.
First off, the universe is not exactly infinite. What scientists mean by "infinite", is that you can keep going in a straight line, and never hit a solid end of the universe.
So, think of the universe as a wheel, a flat surfaced, but round wheel. Now, if we were to go much faster than the speed of light, we could imagine this wheel is a 2d version of the universe. The 2d metaphor works, because you are only traveling in one direction at any one time. If you were to be going forward, but angled up at 20°, you could just imagine the next millimeter of the wheel is at 20°. Now, if you are going straight in any direction in the universe, you will end up back where you started. (If you don't run into an object or die.) So, imagine going in one direction as going around the wheel. You will eventually end up where you started, but never ran into an edge or teleported. You have gone the entire length of the universe. Now, if the universe is expanding, let's have the wheel expand as well. Now that the wheel has expanded, it will take longer to do one full rotation of the wheel, just as it now takes longer to traverse the entire length of the universe. In a 3d world (like our own), pretend that the direction you are going is forward on the wheel, you never change angles, but you end up going in a loop (pretend the wheel is turning instead, like a treadmill).