SOC usually refers to "State Of Charge" which is a measure of the remaining charge left in a battery.
SOC is one of the hardest things to measure, so we resort to approximate methods like measuring the voltage.
There is an approximation for Li-ion batteries that can be used with success if the temperature does not vary too much. If it does, you'll have to measure that too.
The idea is first to make good measurements with decent resolution. I would think a 10 bit ADC should be able to handle this.
Second is to establish a curve with a little testing. Charge the battery, connect a load, make measurements and record the time between measurements. Doing this you can get a feel for what your voltage is vs what your remaining run time is. It is always best to use the actual load that will be used in the end application too.
The equation will at least have a factor and an offset in a form like this:
where v is the voltage of the cell, unloaded for a few hours if possible.
If you intend to include temperature then you will need, as a simple way to handle this, one set of constants A,B for each temperature you measure. So if you measure at say 10, 20, 30, 40, 50, degrees C then you need five A's and five B's and you can use an interpolation formula to get in between values.
That should get you going. As the cell ages however, the A and B will change so you may find the cell running down faster than it did when new. That's hard to figure into the equation, but you might be able to do that by keeping track of the time of discharge and charge and noting any decrease over shorter time periods and then apply that to the formula.
They do make chips that supposedly keep track of the charge and discharge current and thus energy into and out of the battery, but i am not sure how well they work because i have never had to use one.
Another, much more simple way, is to measure the voltage and just display the voltage! If you use three significant digits like 3.86 then you can get an idea how fast the cell will need a recharge as you use the device day in and day out. When you see it get down near 3.60v you probably want to recharge it for example, given a 4.2v max voltage cell.
As you use it day after day you will develop a feel for when it needs to be charged.