It's been about 25 years since I read a story in an anthology. The only details I remember from it are that a guy is told that if, while walking down a road (or something similar), he mentally forces himself to think of dimensions opposite of what they are (down is up, left is right, etc.), he will be able to move into another dimension. He succeeds, but that's all I remember of the story.
"The Gostak and the Doshes" by Miles J. Breuer, M.D.; first published in Amazing Stories, March 1930, reprinted in a number of anthologies and in Avon Fantasy Reader No. 10, 1949 which is available at the Internet Archive. There's a review at Alex Kasman's Mathematical Fiction site. The full text is available at Wikisource.
If you read it in an anthology around 1985, that could have been The Arbor House Treasury of Science Fiction Masterpieces (which was republished in slightly abridged form as Great Tales of Science Fiction), or perhaps Amazing Stories: 60 Years of the Best Science Fiction.
Here is an excerpt from the story:
"According to fiction writers, to switch into the t dimension, some sort of apparatus with an electrical field ought to be necessary. It is not. You need nothing more to rotate into the t dimension than you do to stop the moon and make the trees move as you ride down the road; or than you do to turn the cubes upside down. It is a matter of relativity."
I had ceased trying to wonder or to understand.
"Show me!" was all I could gasp.
"The success of this experiment in changing from the z to the t co-ordinate has depended largely on my lucky discovery of a favourable location. It is just as, when you want the moon to ride the tree-tops successfully, there have to be favourable features in the topography or it won't work. The edge of this building and that little walk between the two rows of Norway poplars seems to be an angle between planes in the z and t dimensions. It seems to slope downward, does it not?—Now walk from here to the end and imagine yourself going upward. That is all. Instead of feeling this building behind and above you, conceive it as behind and below. Just as on your ride by moonlight, you must tell yourself that the moon is not moving while the trees ride by. Can you do that? Go ahead, then." He spoke in a confident tone, as though he knew exactly what would happen.
The title is explained in the Wikipedia article on Gostak:
Gostak is a meaningless noun that is used in the phrase "the gostak distims the doshes", which is an example of how it is possible to derive meaning from the syntax of a sentence even if the referents of the terms are entirely unknown.
[. . . .]
Coined in 1903 by Andrew Ingraham, the sentence became more widely known through its quotation in 1923 by C. K. Ogden and I. A. Richards in their book The Meaning of Meaning (p. 46).
Ogden and Richards refer to Ingraham as an "able but little known writer", and quote his following dialogue:
"Suppose someone to assert: The gostak distims the doshes. You do not know what this means; nor do I. But if we assume that it is English, we know that the doshes are distimmed by the gostak. We know too that one distimmer of doshes is a gostak. If, moreover, the doshes are galloons, we know that some galloons are distimmed by the gostak. And so we may go on, and so we often do go on."
[. . . .]
In Amazing Stories, Dr. Miles Breuer wrote a story, now considered a classic, titled "The Gostak and the Doshes" whose protagonist pops into an alternate world in which the phrase is a political slogan that induces sufficient umbrage throughout the populace to declare justified, righteous war. Other writers have picked up on the reference, notably David Gerrold.
This sounds to me like a Roger Zelazny story, but I'm not quite sure from your description. It could be one of the short stories he wrote in the Amber universe, but it actually makes me think of "Roadmarks", which would be a short book rather than a short story. Hope that helps.
Sounds a bit like Elsewhen from Robert Heinlein, but there are probably too many differences for it to be the one you're looking for.