Front brakes need to be further apart to fit the front wheel through
Here's an annotated rotated version of your photo:



To get the wheel in:


Pull the RUBBER BOOT to the right, slide it along the INNER CABLE toward the PINCH BOLT
Squeeze the BRAKE ARMS together at the top.  This allows the NOODLE to move to the left, permitting the YOKE to swing away from the NOODLE.  When the bike is upside down like yours, it may need a hand.
Release the BRAKE ARMS and they will rotate outwards a lot under spring pressure.  
Now you can install your wheel


To close the brakes back up: 


Make sure the YOKE is dangling downward, toward the tyre.
Squeeze the BRAKE ARMS together, and hold in place with one hand.  An assistant might be needed here.
Manoever the end of the NOODLE into the hole in the YOKE.  Once its seated, gently release the BRAKE ARMS and they should hold their position.
Slide the RUBBER BOOT back onto the end of the YOKE to protect the INNER CABLE.


Do this as soon as you finish putting the wheel in - its very easy to forget and ride off with no brake otherwise !



Other initial setup tasks that will be needed:


You need to adjust the brake pads - they're not at the same height so at least one of them won't be on the rim brake track on the wheel.
The arms appear to be leaning to the bike's left.  There will be a tension adjustment near the brake arm's pivots - either a small philips head screw, or a small hex socket.  When releasing the brake lever, the two arms should move out from the wheel about the same distance.
Also, your brake lever in the initial photo looks like its on the wrong side of the bars - brake levers should be inside your fingers, not at the base of your palms.