Welcome to the world of the mandolin. There's lots of information out there about the history of the instrument and its different incarnations. In a nutshell the mandolin is part of a much larger family of plucked stringed instruments related to the lute. It comes in various forms, such as the more recognisable bowlback versions commonly used in baroque music, and its close cousins famously played in Italian folk traditions, as well as the archtop instruments heard in American bluegrass. There are equivalent mandolins for all the violin family instruments, including mandolas, octave mandolins, mandocellos and the rarer (and much much larger) mandobass.
Here's a quick tour of two common shapes, which are based on the mandolins built by the Gibson company around the turn of the 19th century. The first is what is described as an 'A Style', and the second an 'F Style' which has small variations, but is to all intents and purposes the same instrument:
For tips on how to hold the mandolin, I'd suggest finding videos of a selection of different players and observing their posture, both sitting and standing. Not only is this the easiest way to demonstrate the variety of holds for different shaped instruments (and people!), it'll get you listening and watching from the off. Otherwise take a look at my tune videos page to see how I play; it might not work for you, but might offer a starting point.