How do you estimate the best fit of curve?

You always use some model (i.e. function) to fit experimental curve. If you do not know the kind of curve (linear, parabola, Gauss, etc.) you can try to fit with different functions and then compare the residual sum of squares and coefficient of determination of those fit functions. I use MagicPlot for curve fitting, you can try to find something in MagicPlot on-line help.