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The least aggressive you can be and get the desired result is preferred. I would try a clay bar and a good (I like real Carnauba paste) wax first. If that's not doing it stop back... do you own a power buffer?
No power buffer.....they're expensive and I worry I'll get carried away with it...!
Depending on the severity of the oxidation...often times using a buffer is the best way to go. But if you fear doing more harm than good...then doing it by hand will be an exhausting task. In these economic times...you may find a good used buffer at a pawn shop....and hopefully it is a variable speed buffer.
Using a variable speed buffer will allow you to slow down the speed and reduce the chance of damaging the paint....but is still much faster than doing it by hand. And this in turn will give you confidence to work more "touchy" areas. As long as you follow some basics...using a power buffer is not a problem for a novice. AND the one basic rule that is often times forgotten by a novice is to "pay attention" to what you are doing.
If you are trying to get out as inexpensive as possible...then doing it by hand is the way to go....BUT...you will be spending a lot of hours on it...and it all depends on who much you value your time.
I sort of agree with DUB... it is easier than you might think to mess up with a power buffer, but using one is not "rocket science". It is important to let the weight of the machine, not YOUR weight do the cutting. Keeping the wheel flat against the paint to keep from "catching an edge" and smearing or tearing the paint is vital. Less speed and a super careful approach to sharp edges, and sloped/curved areas is required. I learned to buff when the only pad commonly available was a "****" wool general purpose pad, there are more specialised, less aggressive options now. If the clay bar/ wax treatment fails, research a decent variable speed buffer and Google Mequiar's Liquid Crystal polishes... they're available at many local parts stores, and the system works really well. And they're available in less than gallon jug quantity... saving $$$$.