When properly installing an amplifier a large gauge wire is run from the battery to trunk area. A fuse is installed as close to the battery as possible. The amplifier then connects to that wire. If multiple devices need to connect use a fused distribution block.
Don't forget to run a remote wire from your head unit to the amplifier to turn it on and off when needed.
An automotive battery can range from 9v when fully dead to 12.6v nominally to 13.4v ish when surface charged. An automotive charging system will range from 13.9v to 14.4v normally.
Any component installed into a car needs to be able to handle from 9v to 15v. An automotive amplifier is meant to do just that. Don't use a non automotive amplifier. It will not be happy in a car.
EDIT: There are effectively two answers to your question, an automotive answer and electrical engineering answer and i'm not sure if you'd like either one.
Automotive: No one here develops their own accessories. Accessories are bought already equipped with a power supply that can tolerate an automotive environment. You could try and steal a power brick from existing LEDs or just buy LEDs meant for a car.
Electrical engineering: A DC to DC switching regulator is the best option. Always have a fuse at the input. Then a TVS diode, a zener diode and a MOV all chosen to be just under the maximum input voltage of the DC to DC converter will protect you from spikes. Capacitors at the input of the DC to DC but after the input protection will filter out brown outs. (a couple 220uF aluminum, a couple 10uF and 1uF ceramics ought to do it, output capacitance would also be needed) You might be able to find a prebuitl evaluation kit from Linear Technologies or Texas Instrument. That's all just to make 12v. Then to run a microcontroller you would need a 5 or 3.3v rail and you can accomplish that with a linear regulator like a 7805. A common mode choke or ferrite bead at the input might be nice too.