Otherwise, you can go to Special:Preferences in your Personal tools at the top of any page, click on the second tab ("Appearance"), and select one of "Vector", "Monobook", "Modern" or "Cologne Blue", then press "Save" at the bottom of the page. If you're not sure which skin you use, you can follow the same advice to find out.
Why are you doing this?
The main reason is that the new features we are building – inter-wiki notifications, better ways to patrol new pages, easier-to-use talkpages, and others – mean we have to try to integrate them into all of our skins. We can't replace old software with new software that does not work for a chunk of the community: it's simply not acceptable.
The problem is that because we have so many old skins, building in support for them is expensive in terms of developer time (and so in terms of donor funds). The more time we have to spend making something work with nine or ten different skins, the less we have to build new features or maintain our existing software. It also limits the things we can actually build, since some highly useful features might simply not work with skins from 2001 or 2002. The end result is we have to choose between producing limited software very slowly, breaking the site for a chunk of our community, or switching skins off; we've chosen the third.
Why are you keeping these four skins?
The skins we will currently keep available – Vector, Monobook, Modern and Cologne Blue – were selected because they currently work with the features we provide and/or have active maintainers. Vector is the official skin that we provide and keep up-to-date for all new developments and to fix bugs. The other three (Monobook, Modern and Cologne Blue) are supported primarily by volunteer developers who donate their time to keeping these skins available. We at the Wikimedia Foundation will try to ensure "graceful degradation" for these older three skins, so that newer functionality will work to some extent. Over time, however, if they break we may need to disable those too.
Aren't the old skins better for people on slow connections/computers?
Mostly no. It used to be the case that the ancient skins involved less code and so were better for people with slow computers or poor connections to the Internet. However, since 2011 a technical change means this is no longer true, and the difference is negligible (at most a few kilobytes, or under 5% of a typical page payload).
On the other hand, Vector and Monobook use several background images (unlike, for example, the Classic/Standard skin), which might slightly increase CPU load. Modern and Cologne Blue are free of this issue.
Customized JS/CSS scripts, written to mimic the old skins, will also cause additional download time.
I really like some things about one of the old skins – what can I do?
If you need help, please post clear, actionable, and discrete requests to Tech describing which specific feature from an older skin you would like to see in a newer skin. For example, "I was using the Classic skin and I'd like to use Monobook now. How do I adjust the font to be serif instead of sans-serif?"