While that is a great channel (
https://www.youtube.com/user/rossmanngroup/videos ) I am not sure it is quite a learning one if the person asking the question is like the one you quoted.
Still
Shorted how is the next question.
Some components will fail closed circuit and conduct far more than they did. This is less common than failing open circuit where things lose connection or conduct far less than they did.
If it is shorted solder then first check that the components don't mind it -- many times a chip will have multiple pins going to ground or being grounded and some electronics designers will then common up said pins. No sense getting worried about a perfectly OK design decision.
Anyway visual inspection, possibly with significant magnification (something like a mantis scope is the standard for people doing it for real but a more conventional microscope or even a jeweller's loupe will do in a pinch), is the first step.
If it is not supposed to be shorted then the videos above take care of how to fix it as part of an install, works as well here.
Do also check that the PCB came out OK -- they are made in various ways but often via chemicals which can fail to remove some part of the copper they are supposed to. It is also possible for it to remove too much but that is not short as much as open circuit.
Identifying the component?
They tend to have numbers on top.
They might have part numbers or clues on the board in the silkscreen layer (all the usually white or black text you see on boards, does not have to mean anything but usually does).
https://octopart.com/
https://www.findchips.com/
Some people will make diagrams of the device, nice manufacturers even release them for you (or may be legally compelled to release them in some cases).
If you have a working one then you can compare it.
There are parts identification devices these days too. Though for most you will have to desolder it to test.
Equally if you know what you are doing as far as electronics you can predict what things should be, or at least what they are likely not.
If we are to cover the basics then
electronics companies
Here is my list, most of these are the UK versions but they will have them in most places and might even redirect you there.
http://www.scan.co.uk/
http://www.sparkfun.com/
http://www.ownta.com/
http://proto-pic.co.uk/
http://cpc.farnell.com/
http://www.element14.com/community/index.jspa
http://www.jaycar.co.uk/
http://uk.mouser.com/Home.aspx
http://www.rapidonline.com/
http://www.anglia.com/product_search/product_search/index.asp
http://uk.farnell.com/
http://uk.rs-online.com/web/
http://www.digikey.co.uk/
http://uk.futureelectronics.com/en/Pages/index.aspx?OL=GB&Language=en-GB
http://www.maplin.co.uk/
http://www.pamir.com/
http://bitsbox.co.uk/
http://www.jameco.com/webapp/wcs/st...splay?langId=-1&storeId=10001&catalogId=10001
http://octopart.com/
http://www.findchips.com/
http://ebluar.com/
http://discoazul.co.uk/
http://www.coolcomponents.co.uk/catalog/index.php?cPath=50_74
Many times if you find the failed component then you can change it for that and hopefully get something running again. Other times you might have to figure out what its functionality was and replicate that or exceed it. Indeed basic rule of troubleshooting is check voltages, second is check fuses and generally when looking at circuits you will tend to find people break it down into its functions -- this is the power supply section, this is the input, this is the driver, this is some other output...
Other times still you will want to have some serious electronics knowledge (there is a reason it is considered a profession) but don't get too hung up on that.