How to store audio data for AVR project?
I could transcribe the contents of the many tutorials on this subject here, but I'd rather point you to a very good one that explains the theory and implementation quite well: http://www.nerdkits.com/videos/halloween_huffman_audio/.

In a nutshell, you use PWM to drive the speaker, and you can store the audio samples in a rudimentary compressed format (e.g. huffman coded) in flash (program) memory or eeprom in a symbol table. What I'm saying is, you don't need an external memory chip necessarily depending on the fidelity of the audio and the duration you want to store. Many AVRs have plenty of non-volatile memory for this kind of thing.

If you really need more space than you can get on the AVR itself, you could use an external SPI EEPROM, since just about every AVR has a SPI interface. Just search digikey for "serial memory", go into the "Memory" category, filter down to the serial interface of your choice (e.g. SPI), exclude "RAM" from the "Format - Memory" category and you will still have over 700 devices to choose from. Just pick the cheapest one that is large enough to store what you need, that comes in a package that you are prepared to deal with (I recommend SO-8 for surface mount  beginners).

These all basically work the same way, just read the datasheet to understand the command format. SPI works by dedicating a GPIO pin to the target device to tell it you want to communicate with it (creatively called "chip select" or "/CS"). You just ground that pin and use the AVR's SPI hardware to talk to it per the device datasheets. Browse the web / avrfreaks / github for devices with library support if you want to take a shortcut on software, but honestly we're talking about some pretty simple interface code here.