Can you post an example? It might be more clear if we use a concrete example.
In general, however, the null hypothesis is usually a statement of "equality" between 2 things or among 3 or more things. It also can be a statement of the "absence" of a significant effect, or the fact that a statistic is not significantly different from 0.
The alternative hypothesis is the "opposite" of the null hypothesis, and is what you are trying to show support for (i.e., if there is enough evidence to reject the null hypothesis).
Typically, the alternative hypothesis is a statement of "inequality" between 2 or among 3 or more things, or that an effect is significant, or that a statistic is significantly different from 0.