I Have four question about Laplace transformation.

1. Can anyone show me full but easy example of Laplace transformation. I don't quite understand how transforming some basic functions for example:

2x or x/2 or sqrt(x+1)

2. And what mean parameter S in laplace transformation?

3. Let say I Have very trivial function: 2x and i wanna laplace transform that, is there any integration/derivation type rules how I do it or do i have to memorize transformations or look from the transformation table?

4. Finally, Am I miss something, I understand that with Laplace transformation you can for example digitalize sin / cosine curve and any analogical curve. However if I draw Laplace tranformed function I cant see any digitialization in chart. What Laplace function represents actually?