By clicking on the "my settings" link at the top right of a page on Wikipedia while logged in, you will see other tabs on the new page. Click on the "skin" tab, and you will see a list of skins, such as vector and monobook. You can click the preview link to the right of each skin's name to see how it looks before selecting and saving. Please be reminded that this change may not be seen on all windows or tabs you have open for Wikipedia. In order to do so, you may purge the cache of the page by adding "&action=purge" to the page's url. You may also do so by using your browser's purging shortcuts. en:Cache
You can make changes to the current skin's stylesheet file (CSS) by making a subpage of your userpage named after the skin, with ".css" at the end, such as "User:Example/monobook.css" for the Monobook skin. You may see a message of advice reminding you to purge your cache as well.