Correlation significance help

[The Opiner]

Could someone please inform me as to the procedure used to test the significance of a calculated Pearson's correlation value. An example would be most appreciated. I have not found satisfaction with either the materials I have at hand nor an internet search.

I also am in need of the formula used to calculate Spearman's correlation values, the test for significance for this statistic and guidance on when to use Pearson's and when to use Spearman's.

Thanks in advance.