The parts that you will need are:
5V 70 mA Solar pannel (around 60x60mm)
Twin AAA-size battery holder
2 AAA-size NiMH rechargable batteries (around 1000 mAh works well)
Circuit board (see last step for Eagle files)
2N3906 general purpose PNP transistor (or equivalent)
2N3904 general purpose NPN transistor (or equivalent)
1N5817 low forward voltage schottky diode (general purpose - e.g. 1N914 - diode would probably work)
Ferrite bead/toroid (scavenge from an old compact fluorescent lamp if you only need a few)
LED (high brightness - diffused ideally but I only had water-clear so scratch it up with sandpaper)
1nf ceramic capacitor (some parts of this 'ible refer to a 2n2. Either seems to work fine)
30 cm 22-guage solid copper wire (from an old ethernet or telephone cable works well)
Old (empty) jam or pickle jar to house your circuit (we will assume you are using this).
Sparkly things (e.g. acrylic jewels) for the bottom of the jar (makes it look pretty)
Glass paints (could be included in kit)
Small double-sided sticky pad (optional but useful)
Soldering iron & solder
Drill press or punch
Hot glue gun & glue (epoxy would be fine but slower). I use low-temp hot glue with the kids.
A little tape to hold things in place
Medium grade sandpaper (tiny bit)
Helping-hands type tool also very useful
* These resistors may need adjusting depending upon the performance of your solar cell and LED. The 4K7 and 22K make a voltage divider that controls the light level at which your LED comes on. Increase or leave out the 22K for darkest switch-point. Decrease the to switch on when it's lighter. But be careful - depending on your solar cell you may need a pull-down to make the PNP switch on fully. A 100K trim-pot would probably work well if you wanted to control this.