How do you change the phase of an electromagnetic wave? I was watching a video on how cell service works, and the author talks about three things we can change about a wave.
I understand that changing the amplitude is basically changing the brightness, by adding more power to the transmitter. We can also change the frequency, or the "color" of the wave, by basically exciting the underlying particles.
What I can't understand is how we can change a phase. Like do we interrupt the EM waves somehow to say "This is your new phase?"
 A: The key to understanding the phase changes which occur in cell phone transmissions is to realize that the signals generated by the tower don't look always look like nice easy sine waves.  Take this example from Physics and Radio-Electronics:

Most of the time we're thinking of nice easy sine waves like the first two rows, but when we're adding in phase shifts, the results look more like the bottom.  In their particular example, they've chosen to modulate the phase every time the message signal goes from increasing to decreasing.
Such a circuit can be built rather easily.  When you wish to change the phase by 180 degrees, simply disconnect the wires from the antenna and connect them reversed.  It's easy to see that whenever the voltage would have been $v$, it must now be $-v$.  Obviously physically disconnecting the switches isn't going to fly at the speeds cell phones need.  We can wire up a double-pole double-throw switch to reverse voltages like this:

This starts to automate the process, but still isn't fast enough.  If you get further into electronics, you will learn about devices that can switch a signal millions of times a second... transistors.  These are fast enough.
There is one trick to making these work well.  If you do your 180 degree phase transition at just any time, you might suddenly try to jump from 0.5V to -0.5V.  This introduces all sorts of artifacts as the circuits... well... rebel against the sudden discontinuity.  So cleverly, 180 degree phase shifts are only done at the points where the voltage is 0.  At this voltage, a 180 degree phase shift doesn't change the voltage, but it does change the direction the voltage is going.  (There are similar clever times for doing phase shifts other than 180 degrees)
The other thing to remember is that the cell phones don't have an ultra-accurate reference frequency generator that is magically "in phase" with the tower.  It can determine when the phase shifts (its easy to see in the graph), but it can't tell which phase is supposed to be 0 degrees and which phase is supposed to be 180 degrees.  We typically solve this digitally.  Before sending data, the tower transmits a string of known bits (like 101010101000000).  The cell phone can see the rapid phase shifting in the first part, but can't tell 101 from 010.  It figures out when the transitions take place, but doesn't know which transitions they are.  Then the tower sends several bits worth of data that are all 0.  Now the cellphone can signal that doesn't phase shift for quite some time (several nanoseconds).  Now, because we all agreed on this training signal, we know that those were 0's, and we can get our local signal generator exactly in phase with the towers.  After this, data transmission can take place.
But in the end, its like being out walking your dog on a leash.  If you want to change the direction the dog is walking, you just shift the direction you're leading with the leash.  No need to yank on them (typically).  Its just a change in the forces being applied.
