There is no simple way that is right. The existing WM drain should be 2" drain and the trap should be above the floor, so there are problems going into this. You don't want to put another trap and dump into the standpipe, that will only cause problems and be way wrong. You could dump the sink (w/ the DW connected via a branch tailpiece) into the standpipe, but that would create a tailpiece dropping down farther than code (at least the UPC) allows and would tend toward causing the trap to syphon, a bad thing. The other option is to bust the wall and tie into the vent, but it is probably 1 1/2" and code requires 2" - it is hard to imagine it was run with a 2" vent and a 1 1/2" standpipe. The right way is to find 2" under the floor and re-run the works, tying into the existing vent. I suspect that is not going to happen. Others may disagree, but if the floor isn't going to be nuked, I would lean toward tying into the vent (undersized though it is) and capping the existing standpipe. My thinking is that while the the drain may be prone to backing up, that is better than syphoning the trap.