What kind of brakes are these?

Those are V brakes. You can put the "noodle", the metal bent part which has the cable inside it, over the "noodle holder" on the other brake arm. If it doesn't have enough clearance, you will find a barrel adjuster somewhere (usually at the lever), which you can "tighten" (rotate clockwise) to offer more space for the outer cable, which lessens the tension in the inner cable. Then when the noodle is connected, rotate the barrel adjuster counterclockwise to have enough clearance for good braking.

Note the barrel adjuster usually has not only the main screw but also a lockring. To turn it, you need to loosen the lockring and only then can you turn the main adjuster.