It walks with its three legs.
The 5th Edition Monster Manual gives an image depicting Otyugh locomotion on pg. 8:
Reaching into older editions, the 3.5 Monster Manual contains this description on pg. 204:
The creature shuffles about on three thick, sturdy legs
Reaching back further still, Dragon Magazine #96 published in April of 1985 has a similar description, in the article "The Ecology of Gulguthra" by Ed Greenwood (pg. 21):
An otyugh's body is lumpy, mottled purple, green, and (primarily) brown, and the creature stumps about on three fat legs of similar appearance.