There should be no "white" wire on a switch. The switch (in most cases) is never switching the grounded (neutral, white) conductor. If your switch (a dimmer, remotely controllable??) requires that its red or black wire be connected to the supply side, you'll have to differentiate that. If not, you can connect one black to the red and the other to the black.

I'm going to guess in the "old switch" diagram that the black wire connected to the old switch that's pigtailed with two other blacks and a red is your feed (hot). If this is the case then connect this wire to the black of your new switch. Connect the remaining black to the red of the new switch, green to green, and cap off the 3way wire of the new switch. Done.