Popular Mechanics February 1962 carried this feature anouncing their build your own guitar kit. It was a simple one pickup single cut-away electric with a bolt on neck which sold for $42. I wonder if any of these guitars are still in use today? Here is the article in full:

Jason Lollar has reissued his book, Basic Pickup Winding and Complete Guide to Making Your Own Pickup Winder. You can order it directly from his website. It is on sale for $60 plus shipping.

The Japanese Gakken Mook series is a range of self assembly kits each with an accompanying mook (magazine-book). Kit number 26 is a particularly cool build-it-yourself miniature guitar. The kit has around 20 parts and should take an hour to put together, with the finished 4 string instrument about 15 inches long and 5 inches wide.

Have you every wanted to make your own guitar but have been put off by your lack of wood working skills? A Zoybar could be the solution. It is a modular guitar construction system that simply bolts together.

This is a picture of some handmade guitar picks (plectrums), posted by a member at MAKE.com. They are cut from gift
cards,  credit cards, hotel room keys, etc. Some are made from other materials like cardboard, "Handi Snacks" stick, CD, Toshiba laptop, and plastic
packaging.

Build Your Own Clone sells a good range of guitar DIY guitar effects pedal kits, which are great for the inexperienced maker. Each kit is based on a famous effects pedal and comes with absolutely everything you need to build the pedal. Step by step instructions should make assembly a breeze.

Effects pedals are a great introduction to the world of DIY guitar gear, because:

In Victorian times matchsticks were used as a sort of wooden Lego. Using small pieces as building blocks elaborate structures can be assembled, without the need for specialised woodworking tools. Using this technique Englishman Jack Hall make a guitar, mandolins, ukulele, banjo and other instruments out of matchsticks. The acoustic guitar, made in 1937, used 25,000 matchsticks.