Rivers: The tigers basically behave like pures. Concentrate on current breaks and creek mouths, and any cover that breaks current. In more slack areas, they can be anywhere. The like to cruise behind schools of suckers, but are opportunistic feeders. They will hang in cover like any other predator. These fish can literally be anywhere. Don't always focus on the shoreline. In gentle current, they could be away from shore out in the middle, maybe holding on a bolder or behind a ledge, or even a gravel bar.
Use musky lures, and have a selection of different types and sizes to cover the water column. If you are just starting to buy lures, these are good choices:
Bucktails - great for warmer weather and at night, late spring through early fall...but, don't be afraid to toss them during the colder months. Spinnerbaits, pretty much the same thing. Have a good selection of sizes. Small ones may work when larger ones don't, and vice versa. Always do a figure 8.
Crankbaits - like Jakes, Grandma Lures, and such can be cast or trolled. Muskies, including tigers, often will strike at changes of speeds, so working the crankbait with jerks and pauses often will trigger strikes. But if I had to start off a good crankbait selection, I'd get the Bucher Depth Raider and the Shallow Raider. They're mid sized baits that catch a lot of fish, and will cover the water column from 15' up. Crankbaits are good all year long.
Gliders/Jerkbaits - there are a zillion of them out there, but they offer that same erratic action that triggers strikes. The Phantom Softtail, Magic Makers, and Mantas are good choices. I'm not a Suick fan, but my buddies catch plenty of fish on them. I guess that's a confidence thing with me. These work great when the fish are active...especially cooler/colder months. Another thing about these is that you can either do figure 8s or jig them at the end of your cast. Learn to walk the dog beneath the surface with the gliders, and try different speeds and work different depths. If you aren't seeing fish, slow down. If you get follows, try speeding up to produce a bite. Or, try stopping and letting it sink...my buddy's refer to this as the "death pause" and can be as deadly as a figure 8.
Big Soft Plastics - magnum and regular Bull Dawgs, Super D's, or Chaos Medussas are a must have. They work well when casting deeper water. You can jig them, crank them, or use long pulls. These are great for working deep water (casting). Figure 8's or jigging at the end of the cast too.
Topwater - I like the Whopper Plopper and the Bucher Top Raider. Large prop baits work well, as do walk the dog style baits. Summer is prime time for these. But during colder weather, if they are following gliders and not hitting, try a topwater. At the end of the cast, also do figure 8's, and plunge them deep and work your 8 to the top.
Lakes: During cooler months most of the above applies. During warmer months when lakes develop a thermocline, troll to that depth. Grandmas, Depth Raiders or Jakes for mid depths, Believers (shallow), and Plows for deeper water...
On every cast make sure you do a figure 8 with the bait 2 or 3 times. They will hit will doing it.
Great advice. I can't stress this enough. Even if you are trolling, and you pull your lures in to check them to see if they are fouled, do a figure 8 before bringing the lure into the boat, even if it's fouled. Muskies don't care.
A couple more notes: If you have two rods rigged, have a follow up lure ready especially if you've had a hot follow through multiple 8's. Something different on the next cast to the spot might trigger a bite.
Muskies, including tigers, are very adaptable to their environment. They can handle more current than you'd think. There was a video that someone let me borrow about trolling for muskies, and they had a camera rigged to their down rigger. Muskies would cruise up to their baits with little effort at 5 mph, and actually follow the lures for a long time before hitting or deciding to move off.
Another thing though, is that having a stout XL or XXL longer fishing rod for muskies and the right tackle is very helpful if you're tossing the bigger baits. Not only do these rods make life easier on your shoulders, they're also great for doing those deep figure 8's at boatside.
And finally, persistence pays off. Remember where you had follows or encounters with muskies at various times of the year. Chances are, they'll be there again one day. And worse case scenario, you get to fight some huge northerns!
Good luck!