I'm trying to figure out how can i use arduino to display(on small LCD) battery capacity left in my 3.7V lithium poly battery(like 30% or in bars) which is being charged by solar panel.
I'm new to microcontroller so please if anyone can help.
Depends on the battery. For most batteries you can just read the voltage from them to get a pretty good idea as to how flat they are.
If you measure the voltage over a period of time (while you flatten the battery) then you can work out the curve and the rough capacity at certain voltages.
To measure the voltage of the battery, assuming it's a 5v arduino, you can simply attach the + to an analog input pin and the - to Gnd and then use analog read (value*4.888) to get the voltage of the battery.
battery capacity left in my 3.7V lithium poly battery(like 30% or in bars) which is being charged by solar panel.
Shouldn't be too hard. Just wire the cells positive output to a Arduino analog input pin and read its value. A lithium has a pretty linear discharge voltage. 4.2 vdc is considered 100% and around 3.0 is 0%. Never let a lith battery discharge under 3vdc or you risk damaging the cell. Some cells have internal low voltage cut-off circuitry, but unless you know that for sure it's on you to disconnect when approaching 3vdc.
Arduino required 5V input supply to work which means i've to use extra 5V supply for this....is there any other microcontroller i can use to do the same function but which will run at 3V?
Get a 3.3v nano / nano pro. To run it at 3.3v you'll need a boost regulator (your 3.7v battery will drop to a lower voltage, which requires a boost switching regulator) that will bypass the onboard regulator.
Try purchasing a fuel gauge IC. I'm actually in the process of building a fuel gauge board that communicates using I2C. I thought there might be a demand for this because it should be a lot more accurate than using the ADC.