Scientists collect data from satellites orbiting Earth and special planes that fly into hurricanes. These data are fed into computer models to predict where and when storms will form, how they grow, and where they will go.
Satellites
To monitor hurricanes and other weather events globally, scientists use satellites. There are two types of weather satellites currently used, geostationary and polar-orbiting. Geostationary satellites constantly monitor a given region, such as the Western Hemisphere, by orbiting the equator of the Earth at a matching speed, and are best for short-term forecasts. Polar-orbiting satellites orbit the Earth in a north to south rotation passing near the poles and are best for long-term forecasts.

Forecast models 101
Hurricane forecast models are used to help meteorologists predict where hurricanes will go, when they will get there, and how strong they will be when they hit land. Forecasting is not an exact science. A storm's track and strength can change in just a few hours depending on changes in water temperature, high and low pressure system locations, and other factors. Meteorologists look at forecasts from a variety of models, each based on different assumptions and calculations, in order to make the most accurate forecast of the storm.

For more information, please visit:
NASA – What is a satellite?
NASA’s Hurricane Resources Page
NOAA – Latest Satellite Imagery for the Tropics
NHC Forecast Model Information
Weather Underground – Hurricane Forecast Models