I just picked up a trek 7200. The gear shifters are 1-3 on the left and 1-8 on the right. The first question I asked the guy at my LBS once I tested the bike was " Whats the proper method of changing gears, when going from 1-8 to 2-1. " He told me he would just leaves the left shifter (1-3) in the "2" position at all times. That didn't really help much.
The LBS advice may be good for a 'noob' at least while you're learning how your bike handles. Once you're comfortable with the bike start experimenting with the shifts. Position '1' (small chain ring) will result in very easy pedaling/low speeds. Position '3' (large chain ring) will result in harder pedaling and higher speeds. Find the gear combination that best serves your rate of pedaling (cadence). Avoid cross chaining where you are in position 1 on the front and 8 on the rear or 3 on the front and 1 on the rear. You'll find in general that a shift on the front will require two shifts on the the back to give you an incremental adjustment to accomodate changes in terrain to maintain a steady cadence.
You know that 2-1 is most likely an easier gear than 1-8? How hard or easy it is to pedal in a given gear combination depends on the ratio between the left (front) chain ring and the right (rear) cog. There is some overlap between low-high gears and high-low gears. You don't shift smoothly from one gear to another like you do in your car. For now, you can use 2 on the left for most of your normal cruising or level riding. Use 1 on the left when you are going up hills or against strong winds. Use 3 on the left when you are going downhill or when you want to go very fast. Use 1 through 8 on the right to "fine-tune" or find the most comfortable or most efficient gear. It is probably not so good to use 1-8 or 3-1 (cross-chainining) but don't worry about it too much.
What the nice guy at the bike shop didn't want to tell you is that your "24-speed" bike doesn't really have 24 usable gears. You can only use about 4 or 5 of the rear speeds on each of the front rings. The chain can only move so much side to side and if you put it in an extreme position like the biggest ring on the front and the biggest on the rear it puts abnormal stress that will cause the chain and the gears to wear quickly, and it will not run smoothly.
Also, even if you have 24 usable gears, you don't have 24 unique combinations -- the ratios available from the middle front ring overlap those available from the other two rings. What the guy was getting at when he said just use the middle is that you can get to most of the usable ratios from the middle. The only ones you can't get are the extremes, about two in each direction, and for those you need the other rings.
Also, on every bike I've ever had, there are two front derailleur positions on the middle ring, one for the low gears and one for the high. If I run from lowest to highest on the rear without adjusting the front it makes a terrible racket.
A rule of thumb on shifting on bicycles is do most of the shifting on the right (the 1-8 in your example). Rear derailler shifts are crisper and easier to execute and the result in smaller differences. I would say that most cyclists do over 90% of their shifts on the right.
The left shifts are for more major changes. Sort of think of the right as adjusting and the left as setting the scene. On a triple, I only get down in the small ring (the 1) on the left, on nasty hills. For moderate speeds such as moderate climbs, headwinds and so on, I am in the middle ring (the 2) and for higher speeds I am in the big ring (the 3).
You use the middle chainring for most riding so his advice was sound.The small and large ring give you lower and higher ratios, but there is a lot of overlap between these 3 rangs.
In practice you have the
middle ring, 1 to 8.
small ring, 1-3
large ring 5-8
Avoid riding at extreme crossover gears, these wear out the chain and cogs.
Mine has "21-gears', yet I only use 4, all on the 3rd chain ring.
It is nice however to have the real easy gear options there if you need them on some hills, etc. I do find however it is difficult to tune the bike such that each gear is mostly quiet, so I just concentrate on the top 5 with the 3rd chain ring.