Build a deck around the hot tub so that the deck floor and top of the hot tub are on even ground. Existing decks can be extended to fit around hot tubs.
Dig out a hillside to form a level area to install the hot tub. With the hot tub butted up against the side of the hill, it will look as though it was built into the hillside.
Build a set of steps, perhaps with a platform, to lead up to one side of the hot tub. When this approach is coupled with a hot tub installed against a hill, the built-in look is even more apparent.
Introduce mature or adult plants around a new hot tub; using larger, mature plants, instead of young plants, gives the impression that the hot tub has long been a part of the landscape. Surrounding the hot tub with a hedge or using plants with descending heights, as you move away from the hot tub, may further fool the eye into believing that the hot tub is built in.