My sink will not drain at all right now and the washing machine will not either it just pushes the water back up the drain pipe and out onto the floor. What is going on with it and what needs to be done to fix it?

Sounds like a blocked pipe, get someone in to unblock your drains.

Hope this helps,
Louis.

You have blockage in the drain pipe after the washing machine, likely in your main drain line. You will need to rod out that drain, is there a clean out anywhere?