my specialist subject here :) There are lots of die cutting machines on the market at the moment. The big red Sizziz is being phased out and being replaced by the Ellison Big Shot (Ellison and Sizzix same company). You may find a bargain to be had if you don't mind an older machine, but be warned they are very heavy, they are fairly easy to use by pushing down on a handle. The Big Shot has a handle which you need to turn. Other machines include the Quickutz, Wizard and the DoubleDo. The QK is lighter and handheld, but may cause problems if you have any manual dexterity difficulties. There are newer machines which work like a die cutting machine, but work through the computer so you are not restricted to manufactured dies, other machines such as the Cricut (I think) and the Xyron cutter work through computerised books which allow you to select the size of each shape to be cut.
All of the non-computerised machines work on the same principle, you have to buy separate dies to cut out each shape which can add up to a tidy sum (believe me I am talking from experience). You place the die on the paper or card to be cut and feed the whole lot through the machine the force from the pressure of the rollers or the pressure block is enough for the metal parts of the die to cut through the card etc. The Sizzix and Ellison machines will cut through other materials as well as paper and card (thin veneer, foil, thin metal, fabric etc) The Sizzix sidekick and the Ellison Tag A Long are portable versions of these machines and will not cut other materials. I have loads of links to suppliers etc if you want the bext places to shop if you decide to buy one. Alternatively there are lots of sellers on EBay who sell the die cuts ready cut for you. Would you be using them for cards/scrapbooks or other uses, I may have other advice depending on what you plan to use it for,