There are two main reasons why Native Americans got involved in the wars between European colonial powers. First, they got involved because the Europeans could benefit from their involvement. Second, they got involved because they themselves could (or so they thought) benefit from participating in the wars.
One reason why Native Americans got involved in colonial conflicts was because the Europeans wanted and needed their help. The European powers typically did not have enough people in the Americas to fight large-scale wars. By adding Native Americans to their ranks, they hoped to get an advantage over their enemies. The Native Americans were also more likely to understand how to fight small-scale battles in American terrain whereas the Europeans were more used to large battles on open fields. In both ways, Native Americans could help the Europeans in their wars.
But why would the Native Americans want to fight? The reason for this is that they thought fighting would help them. We have to remember that the Native Americans were not one homogeneous group of people. Instead, they were organized into different tribes, many of whom were hostile to one another. Tribes hoped to use the Europeans to help themselves against their rivals. They hoped that, by helping the Europeans, they would get European help in defeating their own enemies. In this way, the Native Americans thought that participating in European colonial conflicts would help them.
Thus, Native Americans got involved in these conflicts because they thought it would help them and because the Europeans thought that they, too, would benefit from Indian involvement.