This is the route I take:
Assuming you exit the station to the north, walk across the bus station and start on Victoria Street. Go straight on through the first set of lights, bear right at the next junction then turn right at the next junction. Follow the road round to the left, keep straight on and bear left once you can't go straight on any more. This takes you past Buckingham Palace. At the lights turn right down the mall (ideally need to be in lane 3 of 4 here) then go all the way down the mall (take lane 2 initially, as lane 1 filters left up a side street) to the big roundabout at the end (there is a short cycle lane and ASL which can help you get past the inevitable queue of traffic here). Once on the roundabout take the second exit, go up a slight hill and follow this road for about a mile (there will be a bit of a diversion in the middle where they are doing some roadworks which requires you to turn right then swing back left before turning right to rejoin your original road). You have a couple of choices here. Firstly you can follow the road all the way to Euston Road then turn right and you are there. Alternatively, you can turn right a bit earlier on to Torrington Place, the turn here is marked by a little cycle filter lane on the right which brings you on to a two way segregated cycle facility. You follow this over the next junction (Gower St which is one way) and turn next left up Gordon St which brings you on to a junction with Euston Road, with the station diagonally opposite you. You then just go straight on through the junction then pull over after a few yards and walk into the station from the west.