Add double outlet to existing circuit
Since you don't give many specifics I'm going to make a few assumptions: You are in the US and single means one device with two plug-ins and double means two devices with a total of four plug-ins. I'm also assuming that the two wires in the box you are sourcing your power from are black and white with a third bare copper ground. First - make sure to shut down all power at the breaker box. You can then either connect to the unused screws on the powered receptacle attaching black to the same side of the receptacle as the black (hot) and white (neutral) to the other side or you can pigtail the blacks together, the whites together and the bare copper grounds together. If you pigtail you will then have three wires in each pigtail. One for the line coming in, one going to the single outlet and one going to the new double outlet. At the new double outlet you will need to again pigtail black to black, white to white, ground to ground with three wires on each pigtail - one for the line coming in and one for each outlet. Run the two blacks (hot) to the hot side of each outlet - it will be marked. The two whites (neutral) to the other side and the grounds to the ground screws.
Now the most important part. It's nice to add on outlets for convenience but you don't want to overload the circuit. You seem to have a number of outlets here that are running on what appears to be one circuit. It's critical to know what size circuit you are working with (15 or 20 amp) and what is on that circuit. This means not only outlets and lights but more importantly what is plugged into those outlets. You have to consider watts. A 15 amp circuit delivering 120 volts is only rated to handle about 1440 watts (15 x 120 x .8) 20 amp is about 1920. For example a hair dryer pulls between 1300 and 1500 watts. Appliances will indicate how many watts they draw or you can find out online. If you overload the circuit you'll be constantly tripping the breaker and posing a safety risk.
Good luck but be careful and think it through.