The posts above nicely describe ridge regression and its mathematical underpinning. However, they don't address the issue of where ridge regression should be used, compared to other shrinkage methods. It might be so because there are no specific situation where one shrinkage method has been shown to perform better than another. There are many different ways of addressing the issue of multicollinearity among the predictor variables, depending on its source. Ridge regression happens to be one of those methods that addresses the issue of multicollinearity by shrinking (in some cases, shrinking it close to or equal to zero, for large values of the tuning parameter) the coefficient estimates of the highly correlated variables.
Unlike least squares method, ridge regression produces a set of coefficient estimates for different values of the tuning parameter. So, it's advisable to use the results of ridge regession (the set of coefficient estimates) with a model selection technique (such as, cross-validation) to determine the most appropriate model for the given data.