IMHO a chain can have quite a lot of wear before it needs replacing. In the old days, (where I live), the best way of guessing wear was to pull it away from the chain ring and look at the gap. They rarely snap. I have had one go in 30 years.
But it is the cheapest bit to replace, if it does not distribute the load evenly it will wear other components, so how much do you value those ?
The other thing to consider is what you are doing with the bike, I take the old racing chains and put them on my commuter/training bike.
The front chain ring shows wear where you apply most load, two places. Look at the teeth and see if they are the same all the way round, if not its worn. If you leave it on long enough the teeth go like a hook and its difficult to change up and down on the front.
The back cassette is dead easy if you have the right tools. A small device on the Shimano fitting drops in the middle and then you unscrew the locking ring. I did mine by hand. The sprockets lift off, the splines on the shaft and the slots in the rings are arranged so that a monkey can put them on. You can't flip them over. Spacers are important to keep the gaps the same.
If you use only one gear it will wear a lot, if you use a lot of gears you will get less wear. Look at the teeth, do they look the same ? If not its worn. Usually the smallest sprokect gets used least, use it as a reference.
If you have one of the old type bodies on the cassette which unscrews by putting a chain with a leaver attached on it and wrestling it off the LBS might be a better bet, but I have not seen one of those for a while. (Except on one of my bikes).
If you have no problems and you are not racing don't worry about it. If it's jumping and the changer is aligned correctly start looking for bits to replace. May be I'm just a bit tight fisted.
