Points needed to come up with a calibration curve
There is not really a simple answer to this—it depends on what you're doing and what level of error your application can tolerate. If you've characterized the response of your instrument and you know that it's linear within a certain range but the response has a variable offset, even a single-point calibration may be sufficient. On the other hand, if you just built an instrument and have no idea of its response characteristics but need very accurate results, you're best to take measurements at many different points (and over a length of time to see how stable the response is) to accommodate the possibility of non-linear response in the range of interest.

Occasionally, if you need to follow a measurement standard (e.g. the ITS-90 standard for temperature), you may be constrained to doing it a certain way so your data can be directly compared with that of other labs but in general, do enough to get the results you need, but not so much that you're just wasting your time. This might mean taking a few well-separated calibration points to get a ball-park value for an unknown sample, then bracketing the value with more calibration points near it to get a better measurement.