Woods admitted he had spent 45 days in therapy and would return for more treatment on Saturday.
"For 45 days from the end of December to early February I was in inpatient therapy receiving guidance for the issues I'm facing," he told the news conference.
"I have a long way to go. But I've taken my first steps in the right direction."
After the accident in November there was a media frenzy around the revelations.
Woods addressed some of the claims made in the subsequent coverage, denying that he had ever used performance-enhancing drugs or that there had been any incidents of domestic abuse between himself and his wife.
"Some people have made up things that never happened," he said.
"Elin never hit me that night, or any other night," Woods said, referring to the night of the car accident.
"There has never been an episode of domestic violence [in our family]."
A small audience, including his mother, watched Woods give the 13-minute apology, but his wife appeared to be absent.
Woods' image has been severely damaged with the details of his infidelity, with telecommunications company AT&T and consultancy firm Accenture dropping him as a spokesman.
"It's amazing how quickly his life and his career unravelled," Andy Richardson, Al Jazeera's sports presenter, said.
|Woods kissed his mother after delivering his 13-minute statement in Florida [AFP]
"At first, for people who know the brand of Tiger Woods that we have been sold over the last 10 years, it was seemingly unbelievable that he could be involved in this," he said.
"[The sponsors] were buying into the idea that Tiger Woods was the pefect focused sportsman that had no other outside interests and he had a perfect family life - suddenly that was the brand that could no longer be sold."
However, Forbes magazine, which puts the golfer's total worth at $1bn, said recently that his remaining deals with Nike, Electronic Arts and Procter & Gamble's Gillette brand would keep him the world's highest paid athlete in 2010.
Sportswear manufacturer Nike said after the news conference that it "fully supports" Tiger Woods and his family.
"We look forward to him returning to golf," it said in a statement.
Electronic Arts and Gilette said that their relationships with Woods "remained unchanged".
"His words stand on their own. We wish him and his family the best," Gilette said.