I am wanting to run my MP3 player off a rechargeable 12 volt. The MP3 player I have runs off one AAA battery but I need longer battery life. How do I hook it up so it doesn't fry the circuit on the MP3?
Capacity of a battery is not about the voltage it can supply. The capacity is usually given in ampere-hours Ah. You can connect multiple AAA batteries in parallel to get longer battery life. If you really want to use a 12 volt battery try looking up "buck converter".
A regulator built arround LM317 should work well. As i guess the working voltage is 1.5 volts and current required may be few millliamperes which can be adjusted to by the said device. But your player should also work with 1.2 volts which is the default /lowest voltage available when the "Adj" pin is grounded. For circuits, you may refer the datsheet, or search this forum for ample threads with a lot discussions about regulating with LM317.
Cheers
Simplest solution, since you dont seem to mind the battery/supply size, would be to use a 'D' cell instead of the AAA. No components required, and the battery would last many times more.
To improve battery life, best choice would be to use a switching regulator with the 12V battery you have. You can use an LM2575-3.3 to convert the 12V to 3.3V and then use an LM317 to decrease the voltage to 1.5V. You could also use a regulator that converts directly to 1.5V. This way, you have better efficiency. Better efficiency means better battery life.