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What is best estimate and how do i calculate it?

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A best estimate is the best guess that you can give for an answer. It is not really done using a formula, just by comparing things in your mind.
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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 fun

What is the formula for calculating standard error of the estimate?

  In what model? In a linear model, if X is the model matrix, it is the square root of all this: the residual sum of squares from the model * the diagonal values of the in