Do you know on any good reference on Weil bound for charcter sums over algebraic curves. I prefer reference which assume few previous knowlage.

Yes, check out this paper: http://www.math.ias.edu/~avi/PUBLICATIONS/MYPAPERS/CKW11/CKW11.pdf Chapter 8. 


D. R. Kohel and I. E. Shparlinski, `Exponential sums and group generators for elliptic curves over finite fields', Lect. Notes in Comp. Sci., SpringerVerlag, Berlin, 1838 (2000), 395404. 

