"Lions tours are difficult. There is a very short space of time to prepare and try to gel. It is the ultimate challenge," Williams told the Guardian.
"Everyone is writing us off and saying South Africa are red-hot favourites. They are world champions and they've got a pretty phenomenal squad.
"We are going in there as huge underdogs, but looking at the talent in the squad, there is no doubt we are capable of producing something special."
The 33-year-old has already toured twice with the Lions, making four appearances on the 2001 tour of Australia before winning his first Lion Test cap as a replacement in the third and final rubber against the All Blacks four years later.
With 88 international caps and those experiences with the Lions behind him, Williams has a clear idea of how the Lions must approach this month's 10-match tour of the Republic if they are to return home victorious. For Williams, simplicity is the key to success.
"A lot of the senior players on this tour would have gone on the last one in 2005, so they will know what it is about," added Williams.
"There isn't going to be much preparation time, but sometimes that can help because you can't over-complicate things and you have got be very basic. I think that is what a Lions tour is about. You've got good players there and you've got to rely on them to make the right calls.
"In the past, the last two tours anyway, we over-trained and over-complicated things. There were so many coaches involved and they wanted their piece of meat. At that time of the season, with quality players, you don't need it. You don't need to reinvent the wheel.
"They are all quality, international players who just need to be pointed in the right direction. You have got to hit the ground running and the coaches on this tour have worked together a lot. Maybe on the last couple of tours there were lots of different coaches and lots of different ideas."