Do you have any idea how to prepare a Magento online store for a mobile phone?
Hi spletnatrgovina. Welcome to the forums. 
There are various ways to approach mobile web design. You can either have a separate site for mobiles, or you can simply style the site differently for mobiles with CSS. The latter is probably the easiest way, though the former is probably more practical for a large site.
My personal preference is just to use CSS to re-format the page on a small screen. Do you have any preferences? If you go with CSS, check out responsive design.
Aren’t there plugins/extensions/themes or something? I know very little about Magento but one would think…
hi…maybe you can check this out http://www.artio.net/magento-e-commerce/try-magento-e-shop-demo-online...a demo on how to prepare magento online store…