Most distributions have what is called a package manager, which keeps a simple database of the software installed, the version thereof, etc. There is usually a program installed that allows you to change what is installed, and to install new software. Multimedia applications are often NOT installed by default, because they contain "non-free" code. It is often necessary to add a repository (a source of software) for multimedia applications.
If I were to guess about your video stuttering (GUESS, mind you), there are a few possibilities:
1. Graphics card drivers/lack of graphics acceleration.
2. Using an outdated version of whatever software is needed to play videos on Youtube.
3. Too many desktop effects enabled, bogging down the video card/CPU.
Keep in mind, these are guesses. I don't know. Another possibility is that the system IS old or out of date.
If you're using Red Hat Enterprise Linux, the user guide may be found here: https://access.redhat.com/site/docum...erprise_Linux/
If Fedora (a Red Hat variant), check here: http://docs.fedoraproject.org/en-US/index.html
Check for sections about installing software.
If neither of those has the information you need, Google may be your best bet.
Good luck. Don't give up.