Are you looking for a simple circuit to measure your Lithium Ion single cell charging and discharging level? Here is one chip circuit, powered up from the same Lithium Ion battery you want to measure.
This circuit is design to measure 3.7V rechargeable batteries level.
4.2V - 100%; 4V - 80%; 3.8V - 60%; 3.6V - 40%; 3.4V - 20%
LED1 - RED; LED2 - YELLOW; LED3 - YELLOW; LED4 - GREEN; LED5 - GREEN
D1 is used to protect a circuit from the battery being placed wrong way. You can use 1N4007 or something similar.
When this circuit was simulated on LTSpice, I used R1 value 18k, however, after this circuit was soldered on a printBoard, this value was to high, so i had to change it to 15k. It might be because of inaccuracy of the other resistor values.
LM339 datasheet: http://www.onsemi.com/pub_link/Collateral/LM339-D...
The circuit for 12V battery level indicator was found on http://www.electroschematics.com/6868/12v-battery...
but with the changes was made to measure 3.7V batteries.