I mostly cover the UC3842 here. I think that's partly deserved because it's a more specialized and, perhaps, more complicated, confusing chip to use. When you understand it, it's flawless in operation and truely involves only a few support components. When I tell someone to build an entire switching power supply, I say it's as easy as tossing the chip, a MOSFET, a transformer and various diodes, resistors and capacitors in a pile, throwing some molten solder on the pile and turning on power. That's an exageration, but honestly, it's very easy. There's not really any design involved, so your biggest concern is determining a suitable transformer (and windings) to use.
The UC3842 series (family difference: duty cycle and voltage ratings) works by timing on time with respect to the output transistor source current. This is known as current mode control. Above is a typical test circuit. An internal oscillator works through Rt/Ct pin 4, creating a sawtooth wave there. The reset pulse generated triggers an internal latch which turns on the output, pin 6. As output current rises (the load is supposed to be inductive), a ramp (corresponding to current) is expected on pin 3. When pin 3 reaches about 1V, the output is turned off until the oscillator resets it. The switch-off threshold can be controlled with pins 1 and 2, the output and inverting input respectively of an internal op-amp. Thus, the two 10k resistors set the gain at about -1. Thus the adjustable voltage on the 10k pot controls the trigger voltage, and effectively, duty cycle. The current level control, I believe, should be set so that under 1V peak reaches pin 3. Then duty % should control from somewhere around 0 to 100%. The typical datasheet "test" circuit shows more gain for the error amplifier and resistors on either end of the duty % control (more gain, but a narrower voltage range. Same thing.) Bypass capacitors should be present on all voltage pins (Vref, Vin and if needed, a small capacitor on Isense), and they should join to a star ground. This circuit can be used, open loop, to control any PWM circuit.
Here we've added an inductive load and transistor. (Note that, when the transistor turns on, if I've drawn it right, the secondary's voltage goes negative, so no "transformer action" current flows.) When the output transistor turns on, primary current and thus source current starts climbing (according to dI/dt = V/L). This current is sensed by a small resistor, usually under an ohm. When the voltage reaches about 1V, the comparator switches the output off until the RC oscillator resets it. (The output falls in about 30ns, so I would recommend Rg = 100 ohms to slow down the output transistor a bit. Otherwise, turn-on and turn-off spikes (due to stray inductance) will haunt you. The loss in efficiency is negligible.) The turnoff current is determined by a feedback op-amp which compares an internal reference voltage to the external feedback voltage. This allows output regulation. Since the current comparator has a limit of 1V, the circuit is inherently current-limited and cannot be adjusted to sink excessive output current.
If the load inductance is too low (for instance, a badly wound transformer, or you hooked it up backwards, leaving only leakage inductance between the transistor and output filter), it'll respond by turning on in short pulses. Since peak current is high, you'll still get output voltage, and if wired for it, it'll regulate it over some range, too. You must keep your phases in mind when wiring this thing, otherwise you'll get erroneous results like this. A scope helps.
Mind inductance in the source/current sense resistor: obviously, wirewounds need not apply, and even "noninductive" types should be avoided. Otherwise, you'll see gnarly spikes at turn-on and turn-off, depending on transistor and inductance. An RC filter (1k into 100pF, T = RC is 100ns) can be applied before the current sense input on the chip to avoid such spurious results, as shown in the schematic above.
For a regulated output, there are two ways. One is direct feedback from the output voltage to the UC3842, using a resistor divider. If an isolated voltage is needed, an optoisolator can be used, driven by an amplifier and voltage reference (a single transistor and a zener are suitable). The example above is from my induction heater schematics and illustrates this. This method fails for multiple outputs, unless it's acceptable that one output gets more regulation than the others (sometimes useful, for example, tighly regulated +5V and less critical +12, -12, -5V from a computer supply). The other method is to use a tertiary winding on the output transformer, to create a mock supply local to the UC3842.
For line-operated circuits, this tertiary winding is typically used to power the chip itself as well, removing the cost of a low voltage control transformer. Starting current is supplied by a resistor from the main supply rail, which charges a capacitor across the UC3842. When supply voltage reaches 16V (or 8.5V for the 3843 and 3845), the UVLO (Under-Voltage Lock Out) circuitry kicks in and the circuit starts running on stored charge. It only takes a few cycles for the filter capacitors to charge and voila, it supplies itself.
There are plenty of other switchmode controllers out there. The SG3524 is a popular one, or was, until the practically drop-in replacement TL494 surpassed it in computer supplies I've been parting out. The 3524 is fundamentally different from the 3842, and easier to understand. It works by generating a linear sawtooth waveform, and uses a comparator to determine where the reference voltage crosses the oscillator voltage. If reference is low, there's only a short period during which the ramp is less; when reference is high, there's a much longer period, and duty cycle is higher. The output is toggled to generate alternating left and right PWM signals, suitable for a push-pull output stage. (A PP PWM circuit can't work in flyback mode as above, because flyback depends on one half of the cycle being a charge period. With two driven directions, this is lost. What's done is a choke-input filter is used to integrate the PWM signal back to DC.) The oscillator's reset signal blanks the output waveform twice every cycle, limiting duty cycle to a maximum level, to prevent shoot-through.
3524's and the like are commonly found in multi-hundred watt supplies, such as computer supplies (half bridge output topology), car power amps (PP topology DC-DC converter to step 12V up to say, +/-40V for output stage) and so on. And, of course, my induction heater. Since the 3524 generates PWM, it can be used for most any PWM application (buck, boost, flyback, etc.), but it isn't optimal for buck because it can't go to 100% duty cycle, and for forward / boost / flyback converters, there are simpler solutions, such as the UC3842 I've been talking about.