How does AoC work?
Each problem will have an input, which will be some text containing a list of numbers or words or other characters. The values will be different for every user. You will need to write a program to process these as the puzzle says, and output a single short answer.
Check out the 2019 questions if you want some examples!
Where do we solve the problems?
In a repl of course!
How does the website get our answers?
The answer will be a single number or word or string of characters. The website can easily check if it's correct, by processing the input itself.
How does it time how long it takes?
It just times how long from when the problem is released to when you submit a correct answer.