How do you re-size images by users device?

I mean, do you have a way to re-size images to fit a tablet, iPhone, android etc or don't you bother?

You'd have to be a bit more specific. There are multiple ways to do it. You could use responsive web design, percentage values or Javascript.

Do a Google search for "responsive images", "adaptive images", "fluid images", "media queries", and "responsive web design"