There were two main influences on goth fashion: bands and the Batcave.
The main influences here were probably Bauhaus, Siouxsie and the Cure. Other bands were influential later, but in the early period these three bands defined the goth look. Not only were they seen live, and occasionally on television, but pictures of Siouxsie, Pete Murphy, Daniel Ash and co appeared quite regularly in the music press and on their records. Any striking look will attract imitators and Siouxsie in particular spawned a host of clones- in fact she has claimed, with considerable justification, that she invented the goth look, at least for women.
Obviously, individual Bauhaus and Banshees fans were already looking "goth" before the Batcave opened, but the Batcave can probably be held responsible for turning the goth look into a "fashion" as such- it got a lot of exposure in the press, pictures were seen by people around the country and the basic style was copied. Specimen and Alien Sex Fiend, both Batcave bands, were also very influential in the developmdent of the goth look (in particular, Jonny Slut from Specimen- there is a large section in Mick Mercer's Goth Rock book about that).
From an article entitled "The Gloom Generation,"by Suzan Colon which appeared in the July 1997 edition of Details Magazine:
DANIEL ASH: Within six months of starting, Bauhaus started getting the black-wearing audience and seeing the kids dressing up like us. We used to call them the androgynous space demons. Or the wildebeests.
IAN ASTBURY: Some of the bands, like Specimen and Alien Sex Fiend, had jet-black hair, black eyeliner, black fishnets -- a futuristic vampire thing. It came more from glam than from any kind of grave robbing. It was just a reaction against the New Romantics, because they were just so posey and shallow.
IAN ASTBURY: There was also a flirtation with pre-Nazi decadence, that sultry, smoky period from late-'20s Berlin that was very androgynous.
FRED BERGER: The aesthetic was pretty much set by Bauhaus, who were a very gender-ambiguous group. The guys wore makeup and they were pretty, and that carried over to the fashion, which for men was lace, high heels, jewelry, thigh-high boots, fetish clothing. Sometimes skirts, but it wasn't drag. Rozz Williams from Christian Death was gender-bending, but definitely a guy. No drag queen would ever consider these gothic boys to be trannies.
IAN ASTBURY: The archetype for the male was Sid Vicious: black spiky hair and a black leather jacket. For the women it was definitely Siouxsie from the Banshees -- that S&M look with the black fishnets, the black leather thigh-high boots, the pale face paint and the dark makeup, and then the big black spiky hair.
SIOUXSIE: I never wore white face makeup; I was never that clowny looking. Actually, it's funny -- at quite a lot of our concerts, I used to look out and see all these little Robert Smiths.
ROBERT SMITH: The Banshees used to give me so much grief about how I looked in the Cure -- we were a raincoat band, but we were never goth. A lot of the photos of me wearing a rosary or a crucifix or something is exclusive to the eighteen-month period that I was playing with the Banshees, because they determined that I should wear their uniform, which I had to go along with because it wasn't my group. But I enjoyed being in it and I really got on with [bass player Steve] Severin.
SIOUXSIE: Put it down to Robert and Severin together. It's all their fault. Both of them would take my clothes and my jewelry. There were some strange nights going on there, lots of cross dressing and clothes swapping. Except they never had anything I wanted to wear.
Note the apparent discrepancy above between Fred Berger's and Ian Astbury's description of the male "goth look". This is because Astbury is describing the early goth gig-going look, which was essentially punk, whereas Berger is describing the later goth club look. Early goth gigs were often very hectic affairs, and the audience dressed accordingly.