How do I determine the torque required for different bolts, etc.? I am new to the world of torque wrenches and have not purchased one yet. I am suffering from chronic loosening of the left side crank and realize that it may be too late to fix, even with a torque wrench, but I'd like to know how to use one properly before buying.
Understand that there are several different types of torque wrenches -- simple "beam" units with a pointer indicator and a scale, "click" wrenches which emit a sound to indicate when the set torque has been achieved, "slipper" wrenches which slip when the torque has been achieved, and probably some other variations.
Significant features/specs are mode of operation (above), min/max torque measured, accuracy, and the sort of actual wrench attachment allowed (usually some standard socket drive scheme).
Beam wrenches are the cheapest, pretty reliable, but hard to read. (Most of the others you set vs "reading" while using.)
There isn't necessarily a standard: manufacturers should provide you with the specific torques for each of their components: Specialized should give you the torque for frame screws, Shimano for derailleur and shifters, Race Face for the cranks, Hope for the brakes, etc.
It is also possible that the same component has different torque recommendations if they come from different manufacturers (a stem from Thomson and another from Truvativ can have different torques) and sometimes even from the same manufacturer (two different stems from Truvativ can have very different torques recommendations).
Park Tool provides a general table, but you should definitely check the product manual or contact the manufacturer.
Using a torque wrench is pretty simple: if the recommendation is 30 foot/pound, you set the wrench and it "clicks" and either warns you or stops the mechanic force (depending on the model) when you get to that value.
The problem in your crank is probably due to something wrong in the screw/thread or a piece missing (it is common for cranks to have small pieces just to prevent loosening). It is also possible you're not tightening it with enough torque.
Increasingly, manufacturers have started labeling|stamping their parts with their recommended (or required for warranty) torque specifications on the part itself. You will see this as "10N·m" somewhere near the bolts usually.
As far as your crank arm issue, it's unlikely that a torque wrench will fix the issue. Unless you were drastically under tightening the bolts (which is seldom the issue) the usually culprit is damage from riding which the cranks have worked loose. Once this starts, it generally only gets worse and requires replacement of the crank(s) and/or bottom bracket.
As far as method of use it varies since their are several varieties of torque wrench. They vary greatly from types that simply measure the pressure being applied to ones designed to prevent any force above a set amount from being applied.
Torque wrenches were designed to prevent stripped bolts and threads or the damage that over tightening can cause to parts (like clamping with too much force on carbon bits and pieces), they are not designed to somehow exert or multiply force during assembly.
The manufacturer of each part determines the torque specifications. Most manuals and instruction sheets included with parts will list the torque specification of each bolt. Sometimes, on large parts like bottom brackets, the torque spec will be listed somewhere on the part itself.
As for how to use a torque wrench in general: