A breadboard makes it easy to wire up circuits without soldering. You can push wires directly into the holes in the breadboard.
Each row of 5 holes is connected together. Any two wires pushed into holes in the same row will be connected together.
Along the top and bottom of the breadboard are "bus strips" used for power and ground. That makes it easy to know where to plug in a wire if you need to get power or complete a circuit.
Normally you'd plug a power line (like from the Arduino's 5v pin) into the red strip, and ground (from Gnd on the Arduino) into the blue one.
If you can, try to use red wires for power and black wires for ground. That makes it easy to tell which is which. Everything else can be other colors. But if you run out of red and black wires, don't panic, it's okay to use other colors.
Nothing connects across the "trough" in the middle of the breadboard. The bus strips don't connect to each other -- e.g. the blue rail on the top doesn't connect to the blue rail on the bottom, unless you run a wire between them. And the short 5-wire segments don't connect across the center trough either.