To add to Tom:
Steelhead have radial spots on the tail covering top to bottom, nose is more blunt than a salmon, back of the fish looks greenish blue in the water.
Coho have a "right angle" anal fin (as Tom mentioned shape of fin) - tend to have a sliver shine to the lower portion of the caudal and NEVER have spots below the lateral on the caudal fin, back of this fish also looks greenish blue in the water
(most common mistake is early spring when 3# cohos are mistaken for rainbows. I have had guys tell me they caught 11 rainbows and had to throw them all back because they were under 21" they were fishing the same area where I was catching coho after coho and hadn't caught a rainbow in 5 days!! --'cause they are still in the stream!!)
Kings are easy -- caudal is spotted top and bottom, multi colored sides, usually appear black or dark in the water, anal fin is at an obtuse angle (greater than 90 - less than 180 degrees. Inset dark eyes and with the black mouth look like the punk rocker of the salmon species!!
It is common for fishermen to look at the color of the mouth to determine species, however, I encourage new fishermen to look at the whole fish to identify them and the most telling attributes are ..... I believe .... the caudal and anal fins of the various species.
With a little practice you will be able to identify species when the fish first surfaces - long before you can see the color of the mouth.
The other reason I know how to identify them from a distance is because I fish next to Ray and see his fish hitting the net all the time, whereas due to my limited success I rarely get to identify one up close!!!