The universe is more or less "homogeneous" and "isotropic", which means that it is more like a "sphere", but it is a three dimensional sphere.

I do not think we know for sure the size of the universe yet, because we can only probe a small part of it. Whether the universe is finite or infinite, depending on the "curvature" of the universe. Imagine we look at a globe, whose surface is a two dimensional sphere. The globe has a finite surface area, because it has a positive curvature. If we reduce the curvature of the globe, its size gets bigger and bigger. And if the curvature is zero, the globe becomes infinite, because effectively the globe becomes a flat two dimensional plane without boundaries. The universe could be thought of as a three dimensional sphere. We can estimate the size of the universe (if it is indeed finite), by measuring its curvature. This can be done even though we cannot see the entire universe. So far the understanding is that, the curvature of the universe is nearly zero, which means that the universe may as well be infinite, or at least much bigger than what we can see.

No one knows!

Here's what we do know. All of the galaxies we can see are moving away from us and the farther away they are the faster they're moving. Not only are they moving away from us they're actually accelerating (which means they're moving away from us faster and faster over time).

Now, light can only travel so fast and that means that if a galaxy is accelerating enough then we can't see it because the light could never reach us! Based on what we know, it seems that any galaxies more than 93 billion light-years away from us would be impossible to see ( read here ) and in fact the most distant object we've seen is about 13 billion light-years away ( read here ). (A light year is the distance that light can travel in an entire year which turns out to be about 6 trillion miles.)

So what's beyond 93 billion light-years? Maybe there are more galaxies just like our own, or maybe there's something very different. Maybe it goes on and on forever or maybe the universe comes back on itself like a giant circle. Maybe someday we'll know for sure, or maybe it will remain a mystery forever.

Honestly, no one knows.

There is no known edge of the universe. We can see for 14 billion light years, and the reason for that limit is because the universe is only 14 billion years old, and so light has had only 14 billion years to travel. The real universe is probably much bigger than this, and may indeed be infinite. We have no way to know this for sure, however.

When people talk about the size of the universe, they usually mean the size of the observable universe. The observable universe is made up of all the space that we could ever possibly hope to see. The observable universe does have an end, that is set by the speed of light. Since nothing can move faster than the speed of light, no information can possibly reach us from farther away than light could reach. This also gives us the funny situation where the observable universe is constantly getting bigger, since light has more time to travel farther. Right now, the distance from us to the edge of the observable universe is about 46 billion light-years.