Basics of Transistors
Transistors are not hard to understand at the first approximation, and that is good enough to at least understand what's going on in many circuits.

Think of a NPN transistor this way:  You put a little current thru B-E, and that allows a lot of current thru C-E.  The ratio of a lot to a little is the transistor gain, sometimes known as beta and sometimes hFE.  One minor wrinkle is that the B-E path looks like a silicon diode, so will usually drop about 500-700mV.  The C-E path can go down to about 200mV when it would allow more current than the external circuit is providing.  The details go on and on, but you can get a lot done with that simple view of a NPN transistor.

A PNP is the same thing with the polarities flipped around.  The emitter is at the high voltage instead of low.  The control current goes out of the base instead of into it, and the collector current goes out of the collector instead of into it.

Let's stick to bipolar transistors for a bit and understand them first, since that seems to be what you're asking about more.  FETs are equally simple to understand at first approximation, but I don't want to confuse things at this point.

While the model above is useful for understanding most transistor circuits, it suggests a lot of ways transistors can be used that may not be obvious.  The conceptually obvious way to use a NPN is to connect the emitter to ground and the collector to the positive supply with a resistor in series.  Now a little change in base current can cause a large change in the collector voltage.

The tricky part is not in understanding how the transistor works, but to imagine all the cool things you can do with a device that works like that.  Getting into all those would be way too much for a post here.  I suggest you think about the simple model I described above, then look up some common transistor circuit topologies and think how the simple properties of the transistor are utilized to do useful things.

Things to specifically look up and analize according to the simple model are:
Common emitter configuration.  This is the basic amplifier.  A particular issue is how to keep the transistor in the middle of its range to use its amplification capability effectively.  This is called "biasing".

Emitter follower.  Gain is not just making a higher voltage.  In this case you get slightly less voltage but higher current and lower impedance.

Now look at some multi-transistor circuits and try to follow what they are doing, how the transistor is used to advantage, but also what trouble the designer had to go thru to run the transitor in a way to be useful.

When you feel more comfortable, look at more unusual configurations like common base.  Its not often used, but has its specific advantages.