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In surfing slang, the expression goofy foot, also goofy footer, designates one who rides a surfboard with the right foot forward instead of the left, thus reversing the usual way of standing.

In this expression, the choice of the adjective goofy (which means: stupid, silly, daft) seems to be related to prejudice against left-handedness and left-footedness—as explained in the following from Surfboarding Hits Seaside, published in The Oregonian (Portland, Oregon, USA) of Monday 9^th September 1963 [sports section, page 5, column 3]:

Surfing carries over the unfortunate prejudice against lefthanders and leftfooters that dogs most sports. In surfing they’re called “goofy-footers” and they ride the board with the right foot forward.

In fact, before it became a surfing expression, goofy foot had already been used in a sporting context, as a synonym of wrong foot (i.e., probably, left foot), in the following from Reynolds News (London, England) of Sunday 21^st August 1938 [page 16, column 6]:

SOCCER KICKING-OFF WITH WRONG FOOT!
SPORT NEWS IN A LINE O’ TYPE OR TWO
By PAUL IRWIN

Football is kicking-off with the goofy foot this season. Blame the League bosses, whose £100,000 scheme to help the broken-down money-player seems set for a flop like a parcel of wet fish hitting the pavement . . . As a fact, the League have made a hash of quite a lot of things!

Interestingly—although the surfing expression goofy foot(er) most probably has no connection with this film—, in Hawaiian Holiday (1937), a U.S. animated short film produced by Walt Disney, the cartoon dog Goofy rides a surfboard with the right foot forward; and the theatrical-release poster depicts Mickey Mouse and Donald Duck riding a surfboard in such a stance.

These are, in chronological order, the earliest occurrences of the expression goofy foot, also goofy footer, that I have found:

1-: From The Virginian-Pilot (Norfolk, Virginia, USA) of Wednesday 14^th September 1960 [page 17, column 3]—here, the expression goofy foot is a verb:

Donna Made Fine Day For Surf ‘Hot Doggers’
By Frank R. Blackford
Virginian-Pilot Staff Writer

Virginia Beach—A few hours after hurricane Donna crashed through Tidewater, some young surfboard riders paddled out into the mountainous breakers.
It was a day they had been waiting for all summer.
[…]
It takes years to become an expert and the vocabulary is esoteric.
A broken wave is “soup.” A “hot dogger” is a surfboarder with a highly stylized performance. To “goofy foot” means to ride with the right foot forward. Waves are designated “open door” or “closed door,” depending on riding possibilities. A “log jam” means too many surfboarders in one place. A “kuk” is a novice.

2-: From Surf-Riders’ Dictionary, by Kerry Yates, published in The Australian Women’s Weekly (Sydney, New South Wales, Australia) of Wednesday 24^th October 1962 [Supplement, page 3, column 2]:

BODY SHOOTING: Riding a wave without a board.
[…]
DOWN THE MINE: When nose of board goes under the surface and heads for the bottom, throwing the rider.
[…]
GOOFY FOOT: A very good rider who reverses the usual way of standing by putting right foot in front of left.
[…]
GREMLIN: A mythical figure who tips up boards, or a young surfrider with bleached hair.
[…]
LEPRECHAUN: Surfboard-rider under 13 years old.
[…]
MUNCHIE: Any type of food.
[…]
QUASIMODO: Trick riding, with body bent nearly double, with one hand stretched out in front and the other behind.
[…]
TOES-ON-NOSE: Trick riding, standing at front of board with toes curled over the edge.
[…]
WIPEOUT: A dramatic fall off a board when a rider is trying to catch a wave.

3-: From a letter that one Cassie Fern wrote about her two sons, one a rocker, the other a surfie, published in The Australian Women’s Weekly (Sydney, New South Wales, Australia) of Wednesday 5^th December 1962 [page 54, column 2]:

As far as my “surfie” is concerned, the way of the waves is his way—board-riding is his life.
I hear such terms as “toes on nose,” “body shooting,” “wipeout,” “goofy foot,” “down the mine,” and so on.
He apparently has “munchies” for lunch and is in the company of “gremlins” and “leprechauns.”