A parachute cast is usually a slackline presentation downstream. The rod is kept high after the cast so that the fly line and fly descend upon the water like a parachute. The rod tip is then gradually lowered and kept in line with the drifting fly as the fly proceeds through the trout's feeding lane. The parachute cast can also be useful for very close presentations that would be too close for a normal overhead cast. This situation can occur along streambanks and lake edges. You can also employ this technique when fishing over brush along a streambank.
Using a standard overhead cast, stop the cast high on the forward stroke. Allow the line to straighten and bring the rod back to nearly a vertical position in front of your nose. As the flyline settles to the water surface, the rod tip should be nearly straight up. Now bring the rod tip down until it points to the fly. Adjust any slack in the line as necessary. If the fly moves past the fish with no strike, bring the flyline away from the fish by adjusting the rod tip prior to pickup.