Muskies are more prone than other fish to follow a lure up to a boat. This makes it easier to find fish when they are not biting, but these fish can sometimes be hard to catch.
The standard way to try and catch a fish that is following is to make a figure 8 at the side of your boat. The way you do this is to put your rod tip in the water and lead the lure in as big of an 8 shape as you can. Big fish in particular will have a difficult time making a tight turn; so make your 8 as big as you can.
Some people suggest changing the speed or action because they think that the difference may encourage the fish to strike. But the advice that makes the most sense to me is to make the lure continue to do what it was doing when it got the fish's attention.
Keep the figure 8 going for as long as the fish is interested, and then a bit longer. Sometimes the fish will disappear for a minute and then reappear from a different angle.
If it is following for a really long time you might try speeding the lure up, hopefully, if the fish thinks your lure is going to get away it will hit it. I still advise maintaining the lure's speed and action, from when the fish was first interested, for at least a while before speeding up.
Some guys claim to make a figure 8 after each cast. This would certainly result in catching a few fish that you'd miss otherwise, but you'll also be making fewer casts. Fewer casts out to where the fish are is not as good either. I'll usually make an L-shape at the end of my casts, because if a fish is following and it makes a turn I'll be able to see the flash of the fish's turn. If the fish are following a long way behind or very slowly one day it might be a good idea to extend your casts alongside the boat for a little longer than normal.
If a fish hits right at the boat, then it will give you a good fight. You should still net it right away, to prevent tiring it. This will make picture taking more exiting too.
One of the first fish I ever caught followed a minnow bait with 3 sets of hooks right up to the boat. When the fish hit the mouth caught the first hook and the tail came around and got caught in the last hook. The fish then froze and the fight was over.