Connecting the two power rails

The two sets of rails are not internally connected. Since I almost always want at least the grounds connected, I like to use two solid core wires to make the two sides of rails carry the same voltages

Heck, I usually leave these on permanently between projects!

While you're at it, it's a good idea to add some capacitors to the rails. Electrolytic and ceramic capacitors are usually 2.5mm spacing so they fit right in. A 10-100uF electrolytic paired with a 0.1-1uF ceramic on either side will often be enough for most simple circuitry.

Watch Out For Split Rails!

Sometimes you'll get full size breadboards that do not have solid continuous rails. This can really trip up beginners because they are used to the ground strip being solid all the way down, but there's a gap!

Check the silkscreen of the breadboard, if the blue and red lines have a gap, you have a split rail

But some breadboards do not have the nice colored lines so you'll have to test with a multimeter or some other way to verify. Use little wires to jumper over the gap, if you want continuous conductivity

Using Fritzing!

We use Fritzing for our diagrams, which can make it very easy to plan out your breadboarding project without even picking up a wire cutter. It doesn't do simulation or anything, it's just for diagramming - but you can go from schematic to breadboard or the other way around and then also generate PCBs.

For complex projects, it can take a crazy tangle of wires and lets you clearly visualize all the connections!

An extra nicety when prototyping with Fritzing is and that the breadboards pins that are "in use" are highlighted green. This can help remind you of what rows are available for other components

Another handy thing is that you can click on the breadboard rows and they will highlight all the connected pins including other rows that are internally connected through components! For example, Fritzing knows about the internal connection in 12mm tactile switches: