How can I observe the Orionid Meteor Shower? I would like to see the orionids sometime this week (October 20-26, 2013). What is the best way for me to observe them by naked eye?

Also, would I be benefitted by trying to look at them with a telescope or or are they too fast and spontaneous for most amateurs to capture?
While this shower is now largely over, the way to best observe meteors is the same for all showers in principle (including coming showers like the Leonids around November 17 and Geminids around December 14).

The name of most showers reference the name of the constellation their radiant (point in the sky the meteors seem to be coming from) lies in. In the case of the Orionids, this is the constellation of Orion, so look in the general direction of (and around) Orion.

As you suggest, meteors appear unexpectedly and move too fast to be caught with a telescope.  The best way to observe them is to lie down comfortably and use the naked eye.  The key word is "comfortably": find a comfortable reclining garden chair or lilo and lie down.  That's one half of the comfort; the other is to stay warm.  Even when watching the Perseids in summer you're lying still under an open sky, and for the fall/winter showers mentioned here you'll really want to bundle up and perhaps take a thermos with a hot drink.

The comfort is important - there may be several minutes between two meteors and hence lying down is a good way to relax while watching, which will allow you to stay out longer and see more.  It is definitely more relaxed than standing up with your head in your neck.

One other tip for "comfort": many people will enjoy this more in the company of other enthousiasts, and if you're one of them you should consider going out with a few other people.  It will allow you to discuss the meteors just sighted to pass the time between events, or even to help each other to see one (if they're not too fast).