What kind of MCU are you using? If you are using an evaluation board, you can often set a jumper to have the chip jump straight to external memory.

If you are just using a chip, you will have to program the chip to start executing at whatever address location your external memory is located at. Also, keep in mind your interrupt vectors because these will not be changed automatically, you will have to program them to jump to the external location as well.

As far as the EEPROM, I'm not sure what your question is. If you aren't using an "in circuit programmable" eeprom, I don't think you can program it without a programmer because the programming voltage is different from the supply voltage. Otherwise, what difficulties are you talking about?