...What do you use to find live wires?
I don't!
Actually for home and business electrical wiring, I've done so much work in construction and wiring that I can pretty much tell what is what just by looking.
And I always work with the power off.
So pretty rare that I need to test anything so far as home/business wiring goes.
If I do need to test power to something (home/business wiring), my tester of choice is a table lamp, radio, or whatever is handy to plug in. This is usually to be darn sure power is off before I work on something.
If I need to test a wire (low voltage, house voltage, car wiring, whatever...), there are many ways to do this. I might disconnect both ends of the wire from the circuit and use a digital ohm meter. Or an analog meter if there is a "diode" in the circuit. Or a digital meter which has a diode function. (Diodes only allow direct current to flow one direction.) They need more electricity flowing through the circuit to test them than a digital VOM provides. Analog meters will test them or a digital VOM with the diode symbol which looks like the bottom picture here...
http://www.kwanms.com/tech/diode/diode.jpg
BTW - LED's are "light emitting diodes"! Stick the test leads on one way and you will get nothing. The opposite way and you get a reading.
Most of my testing is for low voltage stuff because you can't plug anything in to test it. I mostly use a digital ohm meter for this. And I always disconnect both ends of the wire from the circuit before testing. If you don't do this, there could be a voltage on the wire which could damage the ohm meter. Or there may be other things in the circuit which would give you a false reading.
The other day I was installing a new plug on a trailer. I used a digital voltmeter along with a wiring diagram of what is what on the trailer plug and turned on turn signals, etc. on the truck to verify I was making the correct connections.
Then there is the case where someone runs a bunch of low voltage cables - say 10 four conductor cables going to different rooms and terminating at one spot. But they DIDN'T MARK THE CABLES! In that case I would go around to the rooms and strip each wire and leave them hanging. Then in one room short two wires in that cable. Then go back to the main spot and see which cable had a short on those two wires (using a continuity tester or ohm meter). Then mark that wire. Then on to the next wire...
For problems with a 3-way switch circuit - say it is not working. The way I would go about this is by experience. Most likely problem is light bulb...
Second would be a bad switch. Sometimes you can flip a switch and a bad switch will sound or feel different when flipping it. (If they are old switches, I'll just go ahead and replace both of them.)
Then third most likely problem would be with the light fixture or the wiring just behind the fixture. Lots of heat in there which can do a lot of damage to older wiring. If the insulation crumbles, I'll replace the fixture - maybe some of the wiring to the fixture if needed.
VERY unlikely there would be a problem with the wiring itself. Sometimes there can be a bad connection somewhere. But again I would not test, I would remove covers and take a peek inside. See what HORRORS are awaiting me!
For phone lines, my tester of choice is a phone! There are two tests - dial tone and punch a number to be sure you get a tone (if wires backwards, you will not get a tone). For this "tester" you can get a cheap phone, plug it into a jack, then connect test leads to the jack connections.
For finding where there is a cut or break in a wire, I'll disconnect power - remove wires from the circuit, then use a tone generator and a "through the wall detector". Like this one...
http://www.pimall.com/nais/e.tone.html
Then for appliances which are "dead" - no power (circuit breaker on). I'll use a digital voltmeter and start where the electricity comes in from the power cord, then go from there. For this testing power needs to be on of course.
For testing 120V appliances which are dead. 1st thing I do is find something which is working like a lamp or radio, then plug it into that outlet to be sure there is power to that outlet. Then test the appliance to be sure it is getting power through the cord and then go from there.
For testing a wire running from one room to another, get a long string of wire, connect it to one end, in one room, then run it to the other room, then you can use your ohm meter for testing.
A common problem when repairing electrical/electronic things is that people will suspect/replace whatever they don't understand. Like if there is an electronic "black box" or computer module. They don't understand how it works, so this is what they replace. In reality the things most likely to have problems are mechanical things. These wear out with use. So things like switches, relays, motors, etc.