One way to predict tornadoes is by looking into the computerized models. Here in the United States, we operate several operational forecast models on several scales. So those forecast models that predict the large scale weather patterns down to the smallest in three kilometer scale prediction. By understanding how these larger scale models work and then coupling that understanding with smaller scale tracking data, we are able to make more accurate tornado predictions.
In addition to using computer models, another way to predict tornadoes is by using observational data. Observational data comes from things like live Doppler radar, spotters on the ground, or reports from people who have seen touchdowns or observations of damage after a tornado has struck. Once we have a good idea of what kind of environment will lead to tornadoes, we can start looking for signs that an event may turn dangerous.