It's a oblong pillow that fits under your neck (only) and can be used in conjunction with another pillow if you like (at the base).
I can't find my exact brand, as I got it from my Chiropractor and have no idea where that box is, but it looks a lot like this one: http://www.amazon.com/Carex-Health-Brands-P10900-Cervical/dp/B001AFB4UO/ref=pd_sim_sbs_hpc_1?ie=UTF8&refRID=0C3KEX9DVA6EDSD39VN7 I personally prefer the shorter ones, but ymmv.
Generally speaking, you use these to relieve the strain in your neck muscles, which in turn helps your shoulder muscles as it does the job of helping your neck support your head. Just make sure you find a good, firm pillow. You aren't meant to "sink into" these. It should mostly keep its shape when you lay down, although a little give is okay.
You can use it on your side, just positioned more towards the base of your skull than in support of your neck. It also, however, encourages you to sleep on your back, which is generally a better position for most people.