Is this an Isolation Transformer
 

When I picked up the RCA TV the family was throwing out most of the tools the previous owner had so they let me go through them and I found this little Transformer so I grabbed it. Is it an isolation Transformer or can it be used as one?

You're lucky. That's not only an isolation transformer it's a voltage regulating power transformer. If you have unstable line voltage that would thing will take anything from 95-130V with awful fluctuations (even a lost cycle or 2 of AC) and spit out rock solid 118V.
I have 3 of those style regulating isolation transformers and use them keep my tube sets from blooming when the local grid gets squirrelly.

The only bad thing about it is it's only 120W so it's only good for radios and some lower power monochrome TVs (IIRC if you overload these it's bad for them and output voltage slumps substantially and looses regulation).

This is an isolation transformer with 2 primary (input) windings and one secondary (output) winding. If you wire the primary windings in parallel it will take ~110V as it's input voltage, if you wire the primary windings in series it will take ~240V as it's input voltage. It could be wired either way you'll have to check. If you plan on powering it off 120V you can just plug it in to check...If it's wired for 120V output voltage will be normal, if it's wired for 240V output voltage will be low. You can't damage it with a 120V input.

These style of transformers do tend to make significant audible hum... It'll seem weird at first but you'll eventually get used to it knowing it's normal.

If you want to check that it's isolating properly, just use an ohmmeter (with the transformer not plugged in or connected to anything else) to verify that there is an open circuit between the input and output.

Minor warning abou these constant voltage transformers. They only work at the specified frequency, with a very small tolerance. So you can't use one rated for 60Hz on a 50Hz supply. Nor will they work with a small generator, where the frequency isn't stable.

I'm really happy I finally have an isolation Transformer. Everybody has been saying to get one since I started messing with this stuff. Now here's my question when you're doing testing do you plug what you're working on into the isolation Transformer or do you plug your test equipment into the isolation Transformer?

The short answer is YES.

More accurately you can plug EITHER your test equipment OR your radio/TV project in, BUT NOT BOTH at the same time.
I favor the radio/TV being isolated as test equipment makers (atleast in the SS era) usually didn't make their gear in a way it could prevent a shock Hazzard.
But really it's up to you.

I do recommend checking the isolation with ohm's mode on a DMM...On a normal 50s vintage isolation transformer I used to have it one day developed a spontaneous primary to secondary short....I got shocked a few times off of it before I rechecked it and discovered that it failed....

A GFCI wall outlet is also a good back up to have to catch failures like that.

Usual to plug the radio etc under test into the isolating transformer.

The output of the transformer should float. Neither end grounded.

A GFCI (RCD on this side of The Pond) is of no use on the output side of an isolating transformer. Apart from the rare and special case of a failure of the transfomer itself it doesn't give any extra protection on the input side either.

If working on a hot chassis (live chassis in UK/Europe) set an isolating transformer is essential if you want to connect testgear to the set. Otherwise you can make sure the chassis is conencted to neutral and use a GFCI/RCD.

I just worked on an Emerson portable radio that has a hot chassis yesterday!
I have several sizes of isolation transformers, but I seldom use them. Old habits die hard. Our low voltage, 120 volts is a lot less hazardless.
As an electrician, I believe in GFCI's and all the receptacles that I use when repairing are GFCI equipped, either receptacle or breaker.

Note I said a GFCI wall outlet to imply it's used on the input side of the isolation transformer. If the isolation transformer shorts primary to secondary and the chassis leaks current to ground, and if the transformer is plugged in to a GFCI wall outlet that is built in to the house the GFCI will trip and act as a fail safe if the transformer fails.