Multicollinearity is a condition in which the IVs are very highly correlated (.90 or greater) and singularity is when the IVs are perfectly correlated and one IV is a combination of one or more of the other IVs. Multicollinearity and singularity can be caused by high bivariate correlations (usually of .90 or greater) or by high multivariate correlations. High bivariate correlations are easy to spot by simply running correlations among your IVs. If you do have high bivariate correlations, your problem is easily solved by deleting one of the two variables, but you should check your programming first, often this is a mistake when you created the variables. It's harder to spot high multivariate correlations. To do this, you need to calculate the SMC for each IV. SMC is the squared multiple correlation ( R2 ) of the IV when it serves as the DV which is predicted by the rest of the IVs. Tolerance, a related concept, is calculated by 1-SMC. Tolerance is the proportion of a variable's variance that is not accounted for by the other IVs in the equation. You don't need to worry too much about tolerance in that most programs will not allow a variable to enter the regression model if tolerance is too low.
Statistically, you do not want singularity or multicollinearity because calculation of the regression coefficients is done through matrix inversion. Consequently, if singularity exists, the inversion is impossible, and if multicollinearity exists the inversion is unstable. Logically, you don't want multicollinearity or singularity because if they exist, then your IVs are redundant with one another. In such a case, one IV doesn't add any predictive value over another IV, but you do lose a degree of freedom. As such, having multicollinearity/ singularity can weaken your analysis. In general, you probably wouldn't want to include two IVs that correlate with one another at .70 or greater.
