In order to right align the second and third column, use r instead of l. In the following MWE, I have also removed the fourth column cpacifier (c) as you only need three columns. I have also added \multicolumn{1}{c}{...} in order to center the column headers of the second and third column.
The second table in the MWE ise done using tabularx to make sure that long entries in the first column are automatically split into two or more lines so that the table's with does not exceed the textwidth. In this second table, I have also used rules from the booktabs package. These lines have some vertical white space above and below them.
\documentclass{article}
\usepackage{booktabs}
\usepackage{tabularx}
\begin{document}
\begin{tabular*}{\textwidth}{l @{\extracolsep{\fill}} rr}
\hline
\textbf{Art} & \textbf{Stundensatz} & \textbf{Gesamt} \\
\hline
Doing this & 1,5 à 100 Euro & 150,00 Euro \\
\hline
This \& That & 3 à 100 Euro & 300,00 Euro \\
\hline
Even more stuff and corrections & 3,5 à 100 Euro & 350,00 Euro \\
\hline
Hearing & 1 à 100 Euro & 100,00 Euro \\
\hline
MwSt. in Höhe von 19\% & & 171,00 Euro \\
\hline
Gesamt & & 1071,00 Euro \\
\hline
\end{tabular*}
\bigskip
\begin{tabularx}{\textwidth}{Xrr}
\toprule
\textbf{Art} & \multicolumn{1}{c}{\textbf{Stundensatz}} & \multicolumn{1}{c}{\textbf{Gesamt}} \\
\midrule
Doing this & 1,5 à 100 Euro & 150,00 Euro \\
This \& That & 3 à 100 Euro & 300,00 Euro \\
Even more stuff and corrections & 3,5 à 100 Euro & 350,00 Euro \\
Hearing & 1 à 100 Euro & 100,00 Euro \\
MwSt. in Höhe von 19\% & & 171,00 Euro \\
a very long entry a very long entry a very long entry a very long entry & & \\
\midrule
Gesamt & & 1071,00 Euro \\
\bottomrule
\end{tabularx}
\end{document}
\begin{tabular*}{\textwidth}{l @{\extracolsep{\fill}} rr}instead of\begin{tabular*}{\textwidth}{l @{\extracolsep{\fill}} llc}By the way, you defined 4 columns but only use 3 of themright-centered?flush right,right-alignedorright-justified.