Reset number scheme in latex using enumerate

Nesting enumerate environments is the correct way to do this. But you also need to redefine how the second level enumerate labels are displayed. You can do this by putting the following command into your document preamble (between documentclass and begin{document}:

renewcommand{theenumii}{arabic{enumii}}
renewcommand{labelenumii}{theenumii}

The labels for enumerations are via enumi through enumiv theenumX is responsible for formatting the number and labelenumX calls theenumX and puts any additional formatting around the number on the enumeration.

It can easily be done using the command setlist from the package enumitem.

documentclass{article}
usepackage{enumitem}
setlist[enumerate,2]{label=arabic*.}
begin{document}
begin{enumerate}
    item An item in the first level.
    item Another item in the first level.
    begin{enumerate}
        item An item in the second level.
        item Another item in the second level.
    end{enumerate}
end{enumerate}
end{document}