What's the best way to make an existing website fit for mobile devices(netbooks, mobile phones based on Android, Iphone, Blackberry etc.)?
Make it flexible.
You can detect different device widths with CSS media queries: https://www.w3.org/TR/css3-mediaqueries/#device-width
Less normative explanation: https://mislav.net/2010/04/targeted-css/
Great blog post: https://webdesignerwall.com/general/the-wall-is-redesigned
The CSS3 flexible box model can also be your best friend.