I know a website is built using a CMS, but don't know which one. Any tell-tale signs that will reveal which CMS is being used?
Some CMS will leave traces behind in the HTML generated by them. WordPress for example usually adds something like
<meta name="generator" content="WordPress 2.x.y" />
in the head section.
Other systems do similar things (Vignette often adds an HTML comment at the end of the page), but there is no general rule for that.
Also, having decided to build a website using a CMS, what skills can I expect to have to learn (HTML, CSS, scripting etc)?
You will definitely need to become familiar with HTML and CSS. Depending on the amount of customizations you are planning, you may also need to learn a programming language like PHP, Perl, Python or Java.