rt.representation theory - 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).