Complexity of recursive Fibonacci algorithm
Most of the times, you can represent the recursive algorithms using recursive equations. In this case the recursive equation for this algorithm is $T(n) = T(n-1) + T(n-2) + \Theta(1)$. Then you can find the closed form of the equation using the substitution method or the expansion method (or any other method used to solve recurrences). In this case you get $T(n) = \Theta(\phi^n)$, where $\phi$ is the golden ratio ($\phi = \frac{(1 + \sqrt{5})}{2}$).

If you want to find out more about how to solve recurrences I strongly recommend you to read chapter 4 of Introduction to Algorithms.