Tip #1 Timing Is Everything
While this one may seem really obvious considering you have to time the hatch of any bug you fish, It's a little different with salmonflies. The time of year salmonflies are popping off varies widely depending on your home state or even specific river. The Deschutes river in Oregon sees the peak of it's salmonfly hatch in early - mid May, whereas the Madison river in Montana Won't see it's peak until right around the 4th of July. So with that being said make sure you check with your local fly shop on when your local river sees its big hatch.
Now that you know when the salmonfly hatch starts, this is where things get weird. When I'm fishing salmonflies, I try to avoid the peak of the hatch altogether. For about 1-3 days when all those salmonflies are coming off, the trout have more food than they know what to do with. Picture Thanksgiving dinner. Your family has come from all over bringing all sorts of delectable dishes including some of your favorites, Turkey, Ham, potatoes, casseroles, biscuits, the list goes on. There's no way you can eat all of it. You'll be lucky if you eat a quarter of it. The same goes for these fish. It only takes a few of these massive morsels to make a trout's belly bigger and wider than an NFL football. So what should you do? if you're into nymphing and racking up the numbers. Target the leading edges of the hatch. There may be a few big bugs flying around but nothing crazy. If you're into smacking big dries on the water, target the week or so after prime. When the trout are still looking up, but you don't have to compete with waves of big 'ol salmonflies.
Tip #2 Bang The Banks
Not familiar with the term? Allow me to explain. As the hatch approaches the salmonfly nymphs make their way to shore to climb up on the banks where they crawl out of their old skin and let their newly formed wings dry out while they await they're first flight. The trout know this, and they'll sit under trees, willows, and especially undercut banks waiting for a clumsy salmonfly to lose it's grip and fall in. During this hatch you can see upwards of 20" trout hanging out in water much shallower than you'd expect. Sometimes only a foot or two deep if the trout has adequate cover overhead. So what are you to do? Imitate a clumsy salmonfly! Cast right up close to the bank where all these trout have moved in waiting for their prey, watch your fly closely, and hang on tight!
Tip #3 Golden Stones
There's another member of the party that often gets left out and forgotten during the Salmonfly hatch. The Golden stone is a close relative of the Salmonfly. Usually a bit smaller but still measuring up to 2" long, the golden stone often hatches near or at the same time the salmonflies do. This offers a nice change of pace for the bigger picky trout who have seen wave after wave of orange and black dry flies that often come accompanied with a pointy hook. So if you find yourself being treated to picky trout that check out and refuse your dry fly, they may have sore mouths. Try changing up colors and fish a little smaller with a golden stone and your luck may just shift.
Tip #4 Thick Bugs = Thick line
There's nothing I hate more than broken knots or severed line. You could be fighting the fish of your life. He's jumping out of the water left and right. Giving thrashing headshakes and screaming runs. Then right as you're about to net him... SNAP. Back he goes with your fly still in his mouth. Sound familiar? Luckily with salmonflies, it doesn't have to be that way. When you're fishing a dry fly that's often times up to 2" or even 3" long you can ditch the 4x and 5x tippet. I will regularly fish 3x and sometimes even 2x tippet if I've got the real big flies on. The rule here is don't be to shy. The fish have much less reason to scrutinize your fly for 5x tippet when they're staring at a massive meal.
Tip #5 Enjoy the Hatch!
While it's always great to catch big fish on big dry flies and watch them explode on topwater, you've got to enjoy the hatch while it lasts. This only comes around once a year and will only last a couple weeks. Take some time to appreciate the clouds of massive bugs buzzing around your head. It's not every day you get to see something like this. Take a second to sit back and enjoy the fresh green grass, the cool flowing stream, the birds chirping in the trees, and the clumsy bug that just flew into the side of your head!