The most common model of transistor operation is the current-amplifier model, like all models it is something of a simplification and it represents just one way of viewing the way a transistor works. I'll assume your question is in the context of a typical silicon NPN bipolar junction transistor (BJT) used in a common-emitter configuration.
For switching, I gather that the base needs a certain voltage to allow the current to travel through.
This is more or less correct, however the range of useful voltages is very small - you might as well think of it as fixed at 0.7 volts with tiny variations in normal use. This voltage is usually called Vbe (voltage across base and emitter). So long as the base voltage is enough to allow current into the base, the transistor can begin to operate. The more base current, the more current is able to cross from collector to emitter. like a valve, small amounts of base current allow large amounts of collector current. The ratio is known as the gain and might be 100x. Eventually the collector current reaches a maximum and the transistor is said to be in a saturated state. For switching applications you want to quickly drive the transistor into saturation (turning it "on") by quickly raising the base current to a suitable value.
For amplifying... Can only specific transistors amplify and specific ones switch?
Some transistors are better for some types of use. However many common small-signal transistors are used for both purposes.
are you using the power of your high current feed and in a sense mixing it in with you guitar signal to boost it?
No, that's not a useful way to think about what is happening. Think of a small flow of water turning a valve against a spring and controlling the a larger flow of water. It's about controlling not mixing.
if you had a pot to adjust the signal amplification, what exactly would you be adjusting, the current or voltage supplied.
Both usually. Voltage and current are dependent on one another. In the case of a resistive load they are related by the ohms-law equation V=IR. For a constant R, increasing V increases I (I=V/R).
Lastly I read that you can increase voltage and current with a transistor.
As I said, the most common model for understanding transistor behaviour describes the transistor operation in terms of current amplification. However you can usually find a way of converting a current into a voltage.
Is it possible to increase voltage and current above that of any of the supplies?
The voltage at the collector of a transistor in common emitter configuration cannot be made greater than the supply voltage (Vcc) by the normal operation of the transistor itself.
Note: With an additional inductor you can create a circuit that creates higher voltages but this isn't an intrinsic capability of the transistor itself.
If you have an H-bridge controller that can switch cleanly at a PWM frequency which is sufficiently fast relative to the motor's inductance (the lower the inductance, the faster the PWM must be), driving it with a waveform that's 60% forward and 40% reverse will be a good way to drive it forward at 20% speed; 40% forward 60% reverse will be a good way to drive it backward at 20% speed. If both conditions above are met, driving a motor in this fashion will give a speed response which is much more linear than PWM'ing between driven and "open-circuit", and will also be more energy-efficient. Additionally, trying to drive the motor at a speed which is somewhat slower than it's presently turning will provide regenerative braking [i.e. allow motor energy to be fed reasonably nicely into the supply].
The important thing to note is that running the PWM too fast for the H-bridge controller may waste energy in the H-bridge controller; running it too slow for the motor inductance will increase the amount of energy wasted in the motor. If the PWM is much too slow, driving the motor at half speed may use many times more energy than trying to run it at full speed. If, however, the motor is driven with a fast PWM and the H-bridge can handle it, efficiency may be very good; a stalled motor driven at 75% forward 25% reverse will have about half the torque as would one driven at 100% forward, but will only take about a quarter of the power [about 75% of the time, it will draw about half as much current from the supply as it would if on 100%, and the other 25% of the time it return that same amount of current].
Best Answer
I'm going to simplify the analysis here by discussing FETs (field effect transistors) which are controlled by voltage, and ignoring BJTs (which are controlled in part by current). However, these same circuits can be realized with BJTs, just having to take base current into account when doing certain circuit analyses.
I'll begin by drawing up a very naive amplifier, and explaining how it fails in the situation you predicted, as well as other considerations. I'll then build on it iteratively to show how we would really deal with the issues you mention.
To start, we'll need to acknowledge that a transistor alone is not an amplifier. Amplifiers are devices that are composed of one or more gain elements (vacuum tube, transistor, etc) along with a number of supporting components. I'm going to focus on amplifiers for signal gain, rather than power gain, because that's where my background lies. There are other techniques for dealing with negative signals, such as split rails and push-pull drivers that contain both P- and N-type transistors, that I won't deal with here.
This is on the right track, but it overlooks one major consideration: transistors are analog devices. The channel of a MOSFET is controlled by the voltage between the gate and the source. In an N-channel MOSFET, if you apply a higher voltage to the gate than the source, the transistor's channel begins to conduct1. In this way, a MOSFET behaves as a voltage-controlled current source.
Apply larger and larger voltages, and it conducts more current, until the load begins to limit the current. Notice the use of the words "larger" and "more". Rather than talk about discrete "on" and "off" , we talk about a continuous, analog process.
Let's take a very simple realization of an amplifier, specifically a common source amplifier without feedback or degeneration. The FET is configured to be used as a voltage-controlled current source, and applying that current to a resistor creates an output voltage. This is an inverting amplifier -- when the input voltage goes up, the output voltage does down. This will be important later.
And now let's apply an input sweep just to see how the output behaves:
Disaster! This amplifier is nearly useless for something like audio. When the input is negative, zero, or slightly positive, the output is clipped at the positive rail. When the input is positive above the transistor's threshold voltage (a parameter of the transistor, varying with temperature and manufacturing variations), the output is clipped to ground. There's a tiny little region in which the amplifier is useful:
Let's apply a small signal instead. We do this, for example, by adding a capacitor, which allows an AC signal through, and setting the DC bias through a resistor:
Much better. Except not really. We need a voltage source that perfectly matches the voltage we need for the amplifier to operate (called the operating point). Get the voltage wrong, and your amplifier's output is clipped into a rail and we have a useless circuit. Increase the ambient temperature, threshold voltage shifts, and we've got a useless circuit again.
What if we could make our system find this voltage on its own? Let's add some negative feedback (in a simplified realization).
We now have a resistor linking the output back to the input. If the output voltage is too high, the input DC bias rises, causing the output to be reduced (because it's an inverting amplifier).
This result now gives us a very simplified prototypical amplifier. Here's the key point: It no longer deals with negative signals. Instead, we use AC coupling and feedback to operate it in its forward-biased mode of operation at all times, with a small signal to keep it linear and avoid distortion.
In reality, our amplifiers are much more complex. Even the simple op-amp, five transistors in a prototypical version used to introduce them in a design class, actually has dozens if not more transistors in many practical realizations. The take-away is still the same -- we operate many transistors in a small-signal regime, with feedback used to establish useful parameters of their operating point, like we set the DC bias for the input here.
1 A P-channel MOSFET has the opposite behavior. It conducts when the gate has a lower voltage than the source, but is completely cut off when Vg > Vs.