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The easiest way is to be with someone who has learned and can show you - not only physical differences but behavioral differences.
Short of that, check out Field Guides at the book store or online. It will take a while to learn to see the differences, especially since eash species has variations over it's range. Black rats become gray rats, texas rats, yellow rats, etc - and there are areas where the sub-species intergrade producing color morphs like the "greenish" rats in the Carolinas.
But a couple big differences:
Rat snakes are blocky with flatter sides to their bodies. Their head is more distinct from their neck. Their scales have a central "keel" down them which gives them a slightly rough appearance. They are the biggest of the 3 species - the longest ever recorded was 101 inches; almost 8 1/2 feet. Its a great rarity to find one much over 6 feet. Rat snakes can be almost any color but are mostly to almost completely black in much the eastern and north central US. Corn snakes are also a species of rat snakes and are often called red rat snakes. There are yellow rat snakes in NC and SC to Florida, grey rat snakes in parts of south central US, Texas rat snakes in east texas and adjacent Louisiana - plus about a dozen other species and subspecies

The black rat has distinct square black blotches on it's otherwise white belly. They are the best climbers of the bunch - often times seen in rafters or trees. They sometimes kink their bodies when approached.
Racers can be almost any shade of black, grey or brown and in some areas are greenish (Western U.S.) or even blue (Michigan and adjacent states). They are smooth scaled and sleek appearing. They can move very fast and often do. They are sight hunters so have big round eyes. They sometimes pick their heads up to "look around". Racers do not have black blotches on their bellies as rat and king snakes do. They can and do climb but not as persistently as rat snakes. In my experience you're more likely to find them out in the grass / pasture or under cover, boards or tin for example
King snakes are rather more shiny than the other 2 species - thus their scientific name: Lampropeltis, meaning bright like a lamp "pelt" or skin. They have heads that are less distinct from their thicker necks. They are more burrowers than the other 2 and use their thick neck muscles to push into loose soil. They are more secretive and more nocturnal than the rats or racers. They are less likely to be found out in the open and much less likely to climb. Kingsnakes can be solid black (the subspecies L. g. niger) around southern Indiana, Tennesse etc; or each scale can have a white or cream colored dot as in the speckled subspecies found in Missouri, Arkansas, etc. The dots can partially or fully form thin bands or rings around the snakes body as in the eastern subspecies from NJ down to Florida or the snake can be almost creamy yellow as in the south florida subspecies.
All are widely adapted and will eat a variety of food, from crickets to mammals. Black rats often feed on young squirrels that it plucks from nests in trees and are great mousers - they get right down to the rat/mouse nests and wipe them out. Racers will eat birds and mammals but also feed on frogs and lizards - especially the young. Young racers seem to love big black field crickets

Kingsnakes will eat mice, birds, turtle eggs, lizards and frogs as well as other snakes.
The young of rat snakes and racers are blotched, but the pattern fades with age. Many become solid patterned as adults. King snake babies are very similar to their adult patterns so change less as they grow.