The above graphic is an example the most well known type of weather forecast made using computer model ensembles. What most don't realize is that the same models are used year-round to provide forecast guidance to meteorologists in making their forecasts.
The Chief Meteorologist at WRAL-TV in Raleigh, NC Greg Fishel joined Nate Johnson for a discussion of the change in meteorology from "deterministic models" to "ensemble forecasting" in this video:
This video is part of the WRAL-TV Web Weather Extra series and more can be found on the WRAL-TV website.
For more information on the models used used to forecast the weather, please visit the following websites:
NCEP Ensemble Products
NCEP Model Analyses and Forecasts
European Centre for Medium Range Forecasts Products (The Euro is better than the American models for forecasting the weather in the 4 to 10 day range)
NOAA's Global Forecast System (this one is good up to 48 hours from an event, beyond that, it's crap)
If you are interested in seeing even more models, including current output for the latest model runs, you can visit PSU's e-Wall. Warning...it's a Geekfest of data.
Also, if you are interested in learning more from scratch, Jeff Hay's Habyhints website can get you started on a new hobby if you're interested. It's where I got my start a few years ago.