It is a river I know well although I've not fished it this year.
Assuming you are after trout and not those big silver things I would suggest you park in the Watersmeet car park on the side of the A39. From there fish down as far as the cottage at Myrtleberry or head upstream of Watersmeet. If going upstream I tend to forget the first half mile (very steep banks on the ticket side) and follow the path up over the hill and start where it drops back down to the river at Dumbledon Pool. From there follow the river and it takes you away from the, sometimes busy, path in places. That said there are usually far less walkers above Watersmeet than below anyway.
If you want to fish the bit around Rockford up above Long Pool you are probably best off parking where you can on the roadside in Brendon and walking down the footpath to the top of the fishing. There is very limited parking around Rockford.
For the lower end of the river you can park at the end of Tors Road in Lynmouth and fish up to Vellacotts Pool but I have never found this very good for trout. You can however follow the high path on the true right bank up past Vellacotts to Blackpool Bridge. From there you can scramble down into the river and fish all the way up to Lynrock Bridge. Very few people bother to do this (not even the salmon wormers) so you get usually get this bit to yourself.
Starting at Watersmeet always wins for me because you can get good (but not cheap) tea and cakes at the National Trust tea rooms
Flies - Dry sedgy things or klinks. Small nymphs and spiders. There can at this time of year be millions of black gnats. If there is colour in the water after rain then swinging wets downstream can be fun. Try not to waste too much time on the big still pools where you will see lots of fish unless they are rising well, concentrate on the stickles and rough water
Enjoy
Andy