How would you go about burning a bootloader to atmega 2560?

Using Arduino Microcontrollers
1

I have a blank atmega 2560 chip that has no boot loader. How would burn a boot loader to it?

2

See this page:

I burn a bootloader onto a Mega2560 board there. If you have the chip (not on that exact board) you just need to work out the pinouts. Basically you need MOSI, MISO, SCK, RESET, +5V and GND connected as described there.

3

The 2560 is "unique" in that it's bootloader lives beyond the 64kword limit of several programmer protocols (like stk500v1 used by ArdunioISP.) Several popular inexpensive AVR programmers are known to have problems. Since Nick's solution is designed from the ground up to be able to program the 2560, I can't think of a better solution.