This instructable chronicles my progress through making one as cheaply and easily as possible. Please note: this is not a for dummies guide, it is just what I did and how I did it.
The Ultimate Bluegrass Mandolin Construction Manual by Roger H. Siminoff
If you're interested in more details, or want to build the genuine article, I highly recommend getting your hands on this manual. It is a wealth of knowledge by the man who literally wrote the book on the subject.
The attached instructions from Stewmac.com about assembling their campfire mandolin kit. I didn't do things quite the same as they did, but it's handy to read so you get a good picture of what is involved.
basic woodworking hand tools
heat gun & spray bottle or water pistol for wood bending
dremel tool if you want to get fancy
lots of clamps
3/4" softwood scraps, ideally spruce
3/4" hardwood scraps, I used an old floorboard
1/4" hardwood for the fretboard
4mm plywood, alternatively wood planed to this thickness
an 8" piece of 3/16" steel rod, I found mine in an old dead printer
Mandolin hardware (strings, tuning machines, fretwire, tailpiece, nut)
I was able to do the whole thing for under $45, but if you're not a penny pinching cheapskate such as myself, you can find a kit here.
siminoff.net an excellent source of kits, parts, and information
stewmac.com another great place to find parts
Crystal Forest Mandolins a quick overview of the proper process
Chris Williams' mandolin a more detailed review of a 4 string flat top