The process to calculate RREF involves these key steps: 1. Start with the leftmost non-zero column as a pivot column. 2. Select the pivot element (topmost non-zero element in the pivot column). 3. Use row operations to make the pivot element 1 and all other entries in its column 0. 4. Repeat steps 1-3 for the next column to the right, ignoring rows above the current pivot row. 5. Continue until all pivot columns are processed.