How is the null hypothesis used in hypothesis testing?

Statistical tests compare the observed (or more extreme) values against what would be expected if the null hypothesis were true. If the probability of the observation is high you would retain the null hypothesis, if the probability is low you reject the null hypothesis. The thresholds for high or low probability are usually set arbitrarily at 5%, 1% etc.

Strictly speaking, when rejecting the null hypothesis, you do not accept the alternative hypothesis because it is possible that neither are true and it is the model itself that is wrong.