For step-up vs. step-down, just think of what you're doing to the voltage in the transformer:
240V in, 120V out = Step-down.
120V in, 240V out = Step-up.
When trying to use more powerful U.K. appliances in the U.S. via a transformer, you need to remember that many general-purpose 120V outlets are limited to 15 amps. At 120V that equates to approx. 1800 watts maximum (and you need a suitably large transformer, of course).
One thing to keep in mind is that most U.S. homes do actually have 240V available in them -- It's used for the range, dryer, and some heating or air-conditioning units. With suitable plugs/adapter leads you could run a U.K. hair-dryer directly from one of those 240V outlets.
I always think of it water through a pipe... Voltage is a bit like the width of the pipe and watts is how many "gallons" of water is flowing.
The usual analogy with water which is used in elementary electrical texts is to think of voltage as being equivalent to the
pressure behind the water (in fact we often use another term which makes this comparison clear: e.m.f. -- electro-motive force).
Current (measured in amps) is then equivalent to the rate at which water flows through the pipe (i.e. so many gallons-per-minute). The size of the pipe can then be likened to electrical resistance. If you use a smaller pipe, you need more pressure to make the water flow at the same rate as with a larger pipe. In electrical terms, if you increase the resistance of a circuit the current will decrease, but you can bring the current back up by increasing the voltage (electrical "pressure").
Power (watts) is a measure of how quickly energy is being used (1 watt being equal to 1 joule per second) and is the product of voltage and current.
{*} That's why a 1200-watt hairdryer in the U.K. (240 volts) draws 5 amps of current while a 1200-watt hairdryer in the U.S. (120 volts) draws 10 amps. With only half as much voltage, you need twice as much current to obtain the same amount of heat.
{*} Simplified somewhat because with A.C. there are other factors involved as well, but you don't want to go into that here......