What fooled me when I was learning is that you may have to turn up to 360 degrees even before joining the circuit. The figure on p16 of the VFR guide shows the plane joining from the live side, and you have to turn 180 degrees while descending on the dead side before joining the circuit (at circuit height) at the crosswind point.
If you are coming from the dead side, you should be overhead at 2000 feet as before, turn 180 back to the dead side (remaining at 2000 feet), and then descend to circuit on the dead side as shown in the figure, turning another 180. If you ask ATC nicely (if there is one) they may say you can descend to circuit height while approaching on the dead side, without first crossing the overhead at 2000 feet. However, this is not an overhead join.
If it says SOHJ then you should cross the airfield overhead at 2000 feet unless you've asked before, or you are confident that it's OK to join some other way. Obviously, at many airfields, if it's not busy and there aren't other reasons to insist on SOHJ (noise or whatever), then it may be OK to join crosswind, downwind, base, straight in or whatever. However, if there's a radio, I think it's always smart to ask first (or self-announce).