I've been very lucky with tawnies this year and actually seen four in different locations (two in broad daylight). The best view I got was about 8am in the morning in a clearing at the edge of woodland, and I saw a brief glimpse of one flying into the wood, and I stood motionless for a few moments thinking "nah, couldn't have been..."
Then there was an almighty noise of finch and thrush alarm calls, and it flew back the way it came right in front of me, with a chaffinch, blackbird and song thrush in hot persuit! It disappeared into trees where the din continued, with jays joining in the mobbing.
The other occasions - one time I looked out of the window of my old house, where I regularly heard them hooting, and finally saw one silhoutted against the sky. Another time I was taking a stroll at dusk on a local footpath, and was lucky enough to see two flying around, and most recently saw one roosting at Old Moor nature reserve (this was on a guided walk though, so I was cheating!).
Listening out for mobbing is by far the best way, but otherwise spend a bit of time around the areas where they're hooting and hope for the best, because there's a lot of luck in it!
