I have to replace a dual electrical switch that was previously removed in the kitchen area. The switch is all one unit. One switch is for the dishwasher and the other one is for the garbage disposal under the sink. The switch has two brass color screws on one side and two black screws on the other side. There are two white wires and two black wires coming out of the electrical box. What is the correct way in which this four wires need to be connected to the switch.

Why a switch for the dishwasher? Those switches are both single pole units. However, with white wires it sounds like they are switch looped. Any black tape on the white wires? I would find the DW leads and wire nut them together and use the breaker for the disconnect. Then I would use a standard single pole for the disposal. If they are properly installed loops, the whites should be hot to the switches, put black tape on them.

ma0641, Not sure why. I have done more investigating and found out that the actual cables have four wires: one red, one white, one black and the bare copper. The whites are twisted into a cap screw, same with the bare copper.so, which ones are hot ? The red or black? Which ones get connected to the side with the connecting tab? Please advise, thanks in advance.

Maybe both are hot. I would then surmise that you have a 12 or 14/3 with a common neutral and two breakers or one breaker with 2 hot leads. That is commonly found in an older kitchen. But, you must have an extra wire somewhere if you have more than 1 white or black. Get a test light or multi tester to determine what is hot. If one lead is hot, it would go to the side with the unbroken tab. The other side should have the tab broken off. It works that you can have 1 hot feeding 2 circuits or two hots feeding 2 circuits. White and bare are not switched , white possibly but need to be marked with black tape. BTW you posted this question 2X. Please don't do that since you will be getting many answers to the same posts. There is no need for a DW to have a switch. If you pull the bottom plate off the DW, and then remove the cover over the wire connection, you should see what color wire is for the DW.