Now I'll show you tabulation, the iterative approach to DP (dynamic programming). Instead of starting with the problem you want and recursing down (top-down), you start with the simplest base cases and build up to your answer (bottom-up).
I like to think of it like filling out a table: you know fib(0) = 0 and fib(1) = 1, so you write those down. Then you compute fib(2) using those, then fib(3) using fib(1) and fib(2), and so on until you reach fib(n). You're constructing the solution step-by-step from the ground up. There's no recursion anymore, just loops and arrays.