Hi Ironraven,
The circuit will probably be a really simple one such as shown below, using an Light Dependant Resistor (LDR), a single transistor or darlington, a few resistors (the 470 ohm resistor and LED is replaced with something like a 3 x 47 ohm resistors and 3 LEDs), a variable preset resistor (to set the light value to switch on the LEDs) and the LEDs (shows a single LED in the circuit). The voltage from the NiMh or NiCd cells will probably be unregulated. I would assume about 3.6 v (+Vs) as the garden lamp has 3 NiMh cells stacked in series. The Solar Cell will most likely be something like a 4-4.5 Volt 120-140mA Solar Cell (depending on the solar cell Area) such as here at
http://www.dealextreme.com/details.dx/sku.12391 with a reverse blocking diode at around 0.6V to give the 3.6-4.0V for the NiMh cells. Total Solar power will be around 0.45 Watts assumming the solar cell is this large 8cm by 8cm (the one on the garden light looks to be a lot smaller possibly half the power). The NiMh cells are most likely to be generic 1.2v 600 mAHr AAA cells. Charge time for the cells will be around 6 to 8 hrs in bright sunlight (double this for the smaller solar cell on the garden light).

The LEDs will have a typical power output around 60 mW each giving a total of 180 mW output. Total power for the circuit would be around 0.4 - 0.5 Watts giving roughly about 4-6 hrs lighting use. Efficiency is poor for this type of circuit but the component costs are very small.
Deal Extreme has lots of different Solar Cell Chargers such as this one at
http://www.dealextreme.com/details.dx/sku.4813 being much more flexible in use. With this device you could connect one of these USB LED lights
http://www.dealextreme.com/details.dx/sku.5452 and still power another USB device such a MP3 player or Cell Phone at the same time.
For less than $20 even something like this at
http://www.dealextreme.com/details.dx/sku.9134 will produce more solar power. A video is also available showing the solar charger here at
http://www.youtube.com/watch?v=sl7lgFhNTs8Hope this helps.