The correlation coefficient of two variables in a data sample is their covariance divided by the product of their individual standard deviations. It is a normalized measurement of how the two are linearly related with values beetween -1 and 1.
To calculate de correlation in R you just have to use:
You can use the cor.test( )function to test a single correlation coefficient.
Is possible to have an overview of all the correlation in a correlogram http://www.statmethods.net/advgraphs/correlograms.html