Two layers of thick tights* topped with a dress and a long, warm cardigan. I love public transit, but it makes apparel tricky when we're in the midst of a rainstorm. Jeans inevitably get wet and then take hours to dry, so I avoid them.
I wear my clumpy but warm Uggs (the only time I wear them out in public) while I wait for the bus. A woolly hat (brimmed to keep errant rain drops off my glasses) and a giant scarf help out as well. When I get to work, I shed the extra accessories and swap the boots for a pair of ballet flats. Reverse the process to get home, adding gloves if necessary. Easy-peasy.
*The opaque red tights are from Urban (I remain loyal to my Old Navy tights, but they have a limited color selection, so I'm forced to look elsewhere sometimes) and the lace overlay tights are from Forever 21. I can't find the exact pair online, but they have lots of other fun options and it's worth checking out the selection at your local store. As you would expect, the consistency of their sizing is a bit lacking (I have one pair that is a bit small and one pair that is a bit large), but they don't run easily and they're still nice and comfy.