What is stop-motion animation?
It is an animation technique which doesn't involve filming a moving object, but rather the film is made up of individual photographs that are played in sequence very quickly so as to give the illusion of movement. The subject of the film isn't free-moving and therefore only moves when the film maker physically manipulates the object slightly between each photo being taken. The subject is moved in small increments between each photograph/frame so that when the photos are played as a continuous sequence, it produces a moving image. If the film uses plasticine for the animated subject, then it is called 'claymation'.
What do you need to have a go?
You will need a digital camera or webcam, a computer, animation or video editing software (see below link list for free versions or use Windows Movie Maker - which should be already installed on your computer), a tripod or somewhere to put your camera to keep it still, a set, a subject (e.g. a puppet), and good lighting.
To get started as cheaply as possible, you just need a webcam, a computer (which I assume you already have) and a blob of plasticine.
Ideas to get started:
The subject you can play with can be as simple as a blob of plasticine, but there are plenty of ideas of what you can use. The most advanced can create a puppet from scratch, but the best way to start is to use one or more of the following materials/ideas: clay/plasticine (with or without wire inside to hold the shape), paper (cut-out character for instance), drawings, toys (Lego, building blocks, toy cars) or a whiteboard/chalkboard (with drawings on which you can edit slightly between takes).
If you are stuck for ideas, browse the internet for examples to inspire you. Perhaps get your character(s) to act out your favourite TV or movie scene, or try and animate the character to dance to your favourite song - it's up to you!