English or French translation of Gauss' "Summatio Quarumdam Serierum Singularium"

"The determination of Gauss sums" by Berndt and Evans (Bull. Amer. Math. Soc., Vol. 5, Number 2 (1981), 107-129.) contains an exposition of the original proof due to Gauss. It also includes a short historical outline of various classical and modern proofs due to Dirichlet, Cauchy and others.

there is a German translation: pages 463-495 in: http://www.amazon.co.uk/Untersuchungen-hohere-arithmetik-Chelsea-Publishing/dp/0821842137

An English translation of Baumgart's exposition of Gauss's fourth proof can be found here.