While not saying no, it is not the easiest of projects, nor will the results be much good when you finish it.
You need some external SRAM to hold the samples before you transfer it to the SD card.
I want to build my own enclosure but I have no idea how to mount the tactile buttons because they have no screws or holes to mount them.
The least of your problems but these are PCB mounted switches so you have a PCB or strip board behind the panel and have a plunger arrangement to push them through a hole in the panel.
How should I approach multiplexing inputs for the buttons?
You need some external SRAM to hold the samples before you transfer it to the SD card.
Is this necessary? I've made a test with the wave shield and I was able to play back sounds loaded on the card pretty fast when I pushed a button. For me the issue here is grouping sound files or indexing them in some way so I can create kits of sounds to play back.
Thanks for the valuable information. This is exactly what I was looking for! 8)
What Mike means, if you want to record audio (It's an Sampler, right ?!) You need to buffer the audio, as you cannot write directly to the SD card.
Writing to SD cards is done in blocks of data, the Arduino must sample data for a given amount of time, buffer this in some RAM, and when it's full it opens a block on the SD card and dumps the data, and goes on and on, but that is the basic principle.
You can glue them to a panel with a hole for the tip of the switch. Or you can arrange for them to be mechanically pushed by some key top, much like I did in this project:- http://www.thebox.myzen.co.uk/Hardware/Hexome.html
Although that might be going over the top.