Vrzáňová was born in Prague, Czechoslovakia, in 1931. In addition to figure skating, she also played piano and attended ballet school.
After spending the winter of 1949 at home in Czechoslovakia, her father advised her not to come back from the upcoming World Championships and she agreed. She defected from Czechoslovakia during the 1950 World Championships in London and was eventually offered political asylum. Her mother followed her in March under dramatic circumstances – her plane was hijacked. Her father, a professional cello player, visited them several times, but decided not to leave his country permanently. He was held as a political prisoner for 13 years and forced to work in a coal mine. His daughter did not return to Prague until 1990, after the Velvet Revolution.
In 1969, Vrzáňová married Czech-born innkeeper Pavel Steindler; they adopted two children. They ran the Duck Joint restaurant in New York City, and later the Czech Pavilion. She died on 30 July 2015 at the age of 84 while living in New York City.
Vrzáňová started sports at the age of three when her parents bought her skis. They spent each winter in the Krkonoše mountains. After this tradition was interrupted during World War II, Vrzáňová started figure skating. The training conditions were difficult, as she had to skate in early winter mornings. Her training sessions were held in darkness because of the dim-out regulations. She skated at the open Štvanice Stadium before the sessions for hockey players, or at the CLTK club tennis courts, which were flooded with water and frozen.
In 1946, Vrzáňová became the Czechoslovak junior national champion. In early 1947, she moved to Richmond, London to be coached by Arnold Gerschwiler. In 1947, she won the Czechoslovak national championships and placed 7th at the 1947 World Figure Skating Championships.
Vrzáňová represented Czechoslovakia at the 1948 Winter Olympics. She placed fifth in the event, finishing fifth behind compatriot Jiřina Nekolová.
In 1949, Vrzáňová was awarded the silver medal at the European Championships in Milan and won her first World title in Paris. She seized her chance to win the gold medal as the Olympic runner-up and reigning European champion Eva Pawlik of Austria had dropped out because of a broken boot heel just before the free program. At the event, she was credited as being the first woman to land a double Lutz jump.
After winning the 1950 European Championships, she won a second world title at the 1950 World Championships. She then went on a European tour instead of returning home. She eventually moved to the United States and performed for the traveling show Ice Follies for three years under the name "Aja Zanova" before joining the Ice Capades. She also participated in television ads and other shows. After her husband's death, she worked for the Ice Capades and led New York City's largest public ice rink, the Wollman Rink.
Vrzáňová was inducted into the World Figure Skating Hall of Fame in 2009. In 2009, she also received the title of the Sports Legend of the Czech Republic. In 2012, Czech Foreign Minister Karel Schwarzenberg presented to her the 16th annual Gratias Agit Awards in recognition of those who promote the good name of the Czech Republic abroad.