For as long as we've existed, mankind has been asking the difficult questions of our place in this world: How did it all begin? When? How big is the universe? How will it end? When?
Still today, people ask themselves the same questions. What many may not know, is that most of these questions have meaningful scientific answers now.
How did it all begin?
Everything in the universe (including spacetime itself) was compressed to an extremely tiny pea, which "exploded" out into our existence. I'm writing "explosion" in quotes because space itself expanded, there wasn't (necessarily) anything outside of the expansion. This "explosion" is known as the Big Bang.
13.7 billion years ago.
How big is the Universe?
The exact size is not known, but at the very least 90 billion light years in diameter (from one end to the other). Put differently, at least 45 billion light years in every direction from us (radius). A light year is the distance it takes for light to travel for one year, which is exactly 9460730472580800 meters. Multiply that by 45 billion to get the radius.
(If you expected the answer to be 13.7 billion light years in radius, the reason it's not is due to the expansion of the universe. See the answer to the next question.)
The perhaps most promising current theory, eternal inflation, suggests that the universe is infinite when viewed from the inside (as we see it), but is in fact only a "bubble universe" that looks finite to an outside observer. This discrepancy is due to Einstein's General Relativity. (The infinity of things we can see from the inside, that an outside observer does not see, is explained by the fact that those things are spread across different times to the outside observer. Roughly, with infinite time, the outsider sees the infinity of things we insiders see.)
How will it end?
The universe is still expanding since the big bang. Not only that, the expansion is going faster and faster (accelerating). The expansion doesn't "move out the edge of the universe". Rather, it stretches out space (but not within galaxies, as their gravitational pull overcomes this stretch).
Expansion of space means that the universe is cooling down (temperature wise), implying that the universe will freeze to death. More specifically, the disorder (entropy) increases due to the second law of thermodynamics, which, ultimately, will reach its stable state of complete disorderness. Except for some minor quantum fluctuations, the universe has quite literally come to a halt. The universal clock stops.
Unknown, but existence of intelligence is most likely impossible after years (a 1 followed by 100 zeros. For comparison, a million is 1 followed by 6 zeros, and a billion is 1 followed by 9 zeros). After that time, the last black holes will have evaporated (no suns or other shining objects are left either), and the universe enters the dark era.