I know it seems a little strange to write a tutorial about something as obvious as paper tearing, but I have found a lot of people actually feel nervous when it comes to ripping strips from their patterned papers.
When you are ripping papers with a white core you will find that one side of the tear has a white border while the other side does not. Generally, the piece you tear upward will not have the white showing so you need to keep this in mind when planning how your finished project is going to look.
You can also use the edges of items to tear your paper... the edge of a desk works well as does a deckle ruler like the one below. Many people prefer to use a tool as it gives a lot more control to the direction of the tear.
So now you've torn up all your paper, what do you do with it? Well, one idea is to join strips of different paper together to form a kind of patchwork background. Then you can stamp or embellish over the top for a lovely distressed look. It's a great way to use up all those little scraps of paper you've been hoarding... and yes, I mean you!