From what I can see the waste from the washing machine comes in from the left and the waste from that and the sink exits out to a drain via the pipe to the right.
If the dishwasher is to be positioned to the right of the sink, you could break into the waste pipe on the right after the U trap and fit a similar "T" connection to that of the washing machine. But some dishwasher waste hoses can be much thicker than those of washing machines and finish with a U bend to hook into a drain pipe.
In our house we've three separate drain pipes for the washing machine, dishwasher and sink. I've three pipes running through the wall and terminating above an exterior house drain. It wasn't hard to drill through the wall. I found it easier to have a 2' 6" upright wastepipe against the back wall and hook the dishy drainpipe into it, rather than make a different connection. I'm not fond of a collection of plastic connectors. An enthusastic "pull" on either the washing machine or dishy, to get it out for servicing, could pull the connector off.
What sort of waste pipe does your dishy have if you've bought one already?