Style sheets are a mechanism to define presentational attributes in a document, as it's explained in the "Cascading Style Sheets (CSS)" tutorial. In regard to web design and development, the only style sheet language that really matters is CSS.
If you want to get the grip on this aspect of web design, you can start reading the tutorial mentioned before. But this is only going to contribute with the basic idea of its structure and some elemental knowledge about its usage. In order to learn further, you'll need to acces more material than what's presented in this website. Here I'll recommend this set of CSS tutorials developed by Stefan Mischook.
A client-side script is nothing but a program that's executed in the visitor's computer, once the page hass been retrieved from the server and loaded into the browser. These programs have access to the elements of the document and to some events (like a mouse click), which allow authors to enhance presentation of content and interaction with the user. For example, a client-side script could make the document react to user interaction with animations.
A server-side script is also a program, this time, running on the server machine or, in other words, the computer that hands the document to the browser upon request. These programs are useful to modify a web document just before it's sent to the user, according to variables related to the system or the request. For example, a server-side script could adapt the document according to the location the user is accessing the website from, or display profile preferences for a user that's logged in.
In regard to server-side scripting, there are many different options that have, roughly, the same capabilites. In the server-side languages popularity contest, the winner, by far, is PHP, beating ASP, Java, Python and Ruby, among others. I never used any server-side language other than PHP, so my remmendation here are these PHP tutorials. But you shouldn't have trouble finding tutorials for other languages you prefer.