We have no way of knowing. Billions of light years across that we know about, but we can only guess about what we can't see. Or as Douglas Adams put it..."Space is big. Really big, I mean you might think its a long way down the road to the chemist, but thats just peanuts to space....."
Infinite - whatever that means. And, what shape is it (if that's not a contradiction, in that if something is infinite then it has no borders, so no shape)? Now I'm confused.
The problem, of course is that inorder to assess the size or shape of an object you have to have an external view and an independant scale of measurement, which by definition we can't have with the universe.
Space isn't infinite, it's unbounded (and very big!). In other words, like the Earth, while you never come to an "edge", it has a definite size. Unfortunately (and unlike the Earth) it's also expanding (as far as we can make out) and the we're limited by how far we can see with telescopes, so we can't tell how big it is.