There's a Littlewood-Richardson calculator here: http://math.rutgers.edu/~asbuch/lrcalc/

I usually use the "SchurRings" package in Macaulay 2 ( http://www.math.uiuc.edu/Macaulay2/ ) though. No particular reason why, just that Macaulay 2 is something I am used to using. It's very easy to use, here's an example (it doesn't print correctly on this page) where the 4 in the first command means use 4 variables (so we're working in Gr(4, infinity)).

i1 : S = schurRing(s,4)

o1 = S

o1 : SchurRing

i2 : s_{2,2} * s_{3,1}

o2 = s + s + s + s + s + s + s

  5,3    5,2,1    4,3,1    4,2,2    4,2,1,1    3,3,2    3,2,2,1


o2 : S

1

There's a Littlewood-Richardson calculator here: http://math.rutgers.edu/~asbuch/lrcalc/

I usually use the "SchurRings" package in Macaulay 2 though. No particular reason why, just that Macaulay 2 is something I am used to using.