This tutorial shows you how to run a multiple regression with r.

To learn about checking the regression assumptions you can use these short (60 sec each) tutorials:
Normality:    • R: Checking Normality for Regression ...  
Homoskedasticity:    • R Regression: Checking Homoscedastici...  
Linearity:    • R Regression: Checking Linearity in 6...  
Absence of outliers:    • R: Checking Outliers for Regression i...  
Absence of multicollinearity:    • R: Checking the Absence of Multicolli...