No there is no fee to enter in to the lottery. It is free to enter.
You can directly go to the U.S Goverments official web site in the given period and apply for it with out paying any fees.

You must take note that this lottery is not giving visas to the winners directly but gives a chance to apply for the American PR Visas. After winning the lottery winner will process the visa application. The winner will pay a which may be around US$ 755.
If the winner is married, must pay Diversity processing fee and the visa fees for each eligible family members regardless wether they are accompaning the winner to the USA.

There are some web sites possesing as American Goverments web site and ask for the processing beware of them.
Some people may guarntee that they can make you a winner, also don't trust these people too.