There are traditional methods like electrofishing and tagging. But there are also non-invasive methods such as environmental DNA where you can detect organism prevalence from DNA shed into the ecosystem. Our platform was built specifically to help share that type of science for restoration and remediation projects: https://www.ednaexplorer.org
There's an organization of volunteers who walk the streambed during spawning season and mark nests with colored tape on nearby branches. I assume while they're doing that, they also count the fish somehow? They also put a trap near the end of the stream at certain times of the year and count the fish in the trap - the fish are obviously released from the trap afterwards.