There are several ways to do so. Most Linux distro's provide a Live CD or DVD. Boot your computer from the CD/DVD and you'll experience a complete Linux system. However, it's not possible to save changes inside it's configuration. Also, data can't be saved ín the system. Of course, one save data to other drives, like hard discs or USB sticks.
Live CD/DVD's are useful to test new distro's or new releases of them. They can also be used as install media. Furthermore, they are useful to investigate a broken computer.
A second option to create a portable OS, is to install it to an USB stick. On Pendrive Linux you'll find instructions and software to create thumb drive of choice.
Last but not least, my portable distro of choice. I like Puppy Linux very much. It's a small Linux system with 'light weight' applications. The image file is about 200 MB. As it is a portable OS, it runs from the RAM of it's guest computer. I use it on my netbook with 1 GB RAM. On this configuration, Puppy is rather fast. For minimalists there are some other tiny distro's.
Do you carry a portable OS?