Unfortunately, a Raspberry Pi runs at 3.3V, and this particular EEPROM will disallow programming if it's supplied less than 3.5V... so you'll probably want to use something that operates at 5V (or is at least 5V tolerant)
That EEPROM programmer seems like a fine place to start.
Here's a few other simple DIY eeprom programmers:
http://web.archive.org/web/200902101312 ... re/eeprom/http://www.devrs.com/e/tools.php#toolprgrA lot of these are older designs that assume a PC with a parallel port; nowadays that's harder to get.
The biggest difference between an UVEPROM programmer and an EEPROM programmer is that the latter almost always has a special "key" sequence to enter before each operation; the former often can just be programmed each byte/word in sequence. On the other hand, the MX29F1615 requires high voltage, so looking at UVEPROM designs for a way to drive the Vpp/BYTE line between 10V and 5V might be a good idea.
(I'd be tempted to kleverly misuse a MAX232)Do you have any experience with digital logic at all? Browsing digital logic tutorials might not be a bad idea.
I made an AT28C64 programmer just using the 40-pin PIC18F4520; Oddbloke's design there is very close to suitable for programming the MX29F1615 too. (again, except for the Vpp/BYTE line).
The only thing I really have to say about Oddbloke's design is that it assumes that shuffling bits around in software is still fast enough to not matter; that's unfortunately
not my experience. Connecting the address lines and data lines in order to the Atmega's output ports will make things easier.