Playing a fish on a fly rod can be boiled down into simply making the fish work against the spring of the rod until it becomes tired enough to net.
After the fish takes your fly, try to reel in excess line as soon as possible. Tension can be maintained by keeping the line pinched between the handle and your index finger. Feel free to pause reeling and let line out as needed. Finding the right balance between keeping the line tight and letting the fish run comes with experience.