Cloud storage and social media has become so robust, they have nearly eliminated the need for file compression for the common consumer. With most mainstream services being accessed from mobile platforms with little or no compression support, and even more bandwidth than ever file compression seems to be going the way of the pager.
There is, however, still a need for file compression on a commercial level. Large files are often compressed via file sharing services before the user can download them. However, when file sharing services are not available, or you need to send several files together, then the user must return to using a file compression program. Fortunately, the consumer programs are still being developed, and are fully supported by modern operating systems.
For most users, we recommend the open source project 7Zip, which is available for free for Windows, and there are even "unofficial" ports to Linux and Mac. 7Zip is very powerful yet lightweight, and fairly easy to use. You can select a group of files or folders, right click, and add to a ZIP archive. Adding files is as easy as adding files to any folder in windows. Simply click and drag files to add them to the archive.
A slightly more user friendly program for Windows is WinRAR. Similar in most respects to 7Zip, but it's free only for a trial period of 40 days, which is enforced only through an honor system; it does not stop working after 40 days, and there is nothing preventing you from continuing to use it for free. There are also Linux and Mac versions, but they're command line only, which can be quite irritating for the inexperienced user.