Williams said her achievement had yet to sink in and admitted she had to ask her coach to find out whether she had won.
"It's like I've been put into a bubble and I'm just floating around. I don't think my feet are on the ground yet," she told BBC Sport's Clare Balding.
"I feel quite shy, I'm not sure what to do with myself. It's my first win and to do it here at the Olympics - I'm on cloud nine.
"I tried to look at the clock on the side, I saw the number three so I presumed I had dropped down. I had to whisper to the coach 'where did I come?' and he told me I was Olympic champion.
"There have been no celebratory drinks yet, I'm not allowed any alcohol, so I'll save myself for when I get home. When I'm home I'm going to do as much as possible and go to as many events as I can."
Prime Minister Gordon Brown was among those to pay tribute to the achievement of Team GB's newest star.
"I am delighted at Amy's victory in the women's skeleton last night," Brown said in a statement.
"I congratulate her for winning Britain's first solo Winter Olympics gold medal, a first women's gold medal since 1952 and a first since Robin Cousins' successes.
"Shattering the track record she set in her first runs just adds to this major achievement and made for a truly exciting final."
Sports Minister Gerry Sutcliffe added: "The first British individual gold medal at the Winter Olympics for 30 years is an outstanding achievement for Amy Williams, Team GB, and all those in her sport and behind the scenes who have contributed to the win.
"In the dark and chilly days of a British winter, this is a big ray of sunshine.
"I hope it will inspire many young men and women to want to follow her example and aim to become Olympic stars of the future.
"Lottery funding, and the backing of UK Sport and the English Institute of Sport, has been a big factor in Amy's win and I hope this fantastic result will encourage more people to have a go at winter sports."
Team GB chef de mission Andy Hunt, looking ahead to the team's remaining medal prospects, said: "We're not finished yet, I really hope we haven't.
"It has been a fantastic night, fantastic for Amy, fantastic for Team GB and for the country. A gold is truly, truly exceptional.
Olympic champion sister's excitement at win
"We've still got some more opportunities. Our bobsleigh men and women are in good form, so there should be some good performances there and then on to short track and Jon Eley in the 500 metres and the curling, where we've had a great day again today."
Pre-Games, Hunt had said that matching the silver medal won in Turin by Shelley Rudman would represent a success in Vancouver and that anything above that would be a bonus.
Now he hopes Williams' gold medal success can bring about a new era in Winter Olympic sports for Britain.
"Of course we want to build on the medal tally but we have achieved what we wanted to do. This a catalyst for a real uplift in focus and funding and perhaps a performance approach into winter sports."
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