How is the order of a point calculated for elliptic curves over GF(p)
The Schoof–Elkies–Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a finite field. The complexity of this method is in order ${\log^4 p}$. Using SEA you can easily compute the order of group, then with binary multiplication method you can compute the order of arbitrary points. For the meaning of "good"(and another questions), you should read about attacks against elliptic curves.

For more details you can see "Guide to Elliptic
Curve Cryptography, Darrel Hankerson, Alfred Menezes, Scott Vanstone" which is easy and complete book.