What is the standard resolution of singularities, for the nilpotent cone (of the adjoint representation) for the symplectic group? I know how to do this for the general linear group, but am having trouble finding a good reference for the symplectic group. I understand it uses Richardson orbits. 
(I do know what the closure ordering should be though). 



Resolution of singularities for nilpotent cone of the symplectic group
Ben gave the general answer above. If you care specifically about the symplectic group and are interested in a "flag-like" description of its flag variety, then one exists. It is given by all half-flags of isotropic subspaces (this is just like for $SL\_n$, the symplectic group acts transitively and the stabilizer of the standard half-flag will be the standard Borel). With this description, it's just as straightforward computing Springer fibers and the like as it is for the $SL\_n$ case, which you're presumably familiar with.


A reference for these flag-like descriptions can be found in the section of Fulton and Harris on "Homogeneous Spaces" (there's a similar description for the special orthogonal groups).


