SCHEMATICS:

The entire circuit  runs on a 1.2V NiMh battery which gets charged by a 2V solar panel. The board has got a qf5252 ic. This is a tiny but very interesting ic which serves as a switching boost converter and solar charge controller. It only need and external inductor for boosting a 1.2 volt NiMh battery sufficiently high to light LEDs. It runs at a frequency of around 100 Khz.

I filtered the spikes from the boost converter and added an astable multivibrator to blink two leds alternatively to make it more fun for kids. This blinking mode can be disabled with a switch so that the lantern will glow continuously.