Most modern graphical distributions of Linux (e.g. Ubuntu, Fedora) will come with a utility to unpack various types of archive. See your distribution's documentation for instructions on using these programs.
The LinuxQuestions wiki provides a guide to the commonly available terminal commands for archive extraction.
On Mac OS X
Normally when you are on a macOS system and you identify a compressed (i.e. .zip file) in an open folder all you need to do (in 95% of the cases) is just to double click the compressed file that the Archive Utility will automatically uncompress your file into a folder, with the same name of the file.
Most recent versions of Windows come with built-in support for zip archives. On XP, for example, you can browse the contents of said files and click the 'Extract all files...' link in the explorer sidebar. Following the wizard will allow you to extract the archive's contents to another folder.
Unfortunately Windows does not natively support a number of alternative (often better) archive formats. If you encounter a file ending with .rar, .7z, .bz2, .tar or a number of other extensions you should be able to extract these using 7zip or PeaZip. When installing these programs be careful to ensure that they don't steal associations with files extensions that you don't want them to have.
Both of these programs allow you to add an entry to the context (right click) menu. Take 7zip for an example. If, having installed 7zip, you want to unpack a 7z file you can right click on it and open the 7zip submenu. This will present you with a variety of options. Clicking 'Extract to /<name of 7z file>' will extract the archive to a folder of the same name in the same place.