The U values are representations of residual variance - we'll get to that in a few minutes. The method of path analysis is simply multiple regression, so you already know how to do it. The key is in understanding how to outline a path diagram and apply a regression analysis to it. Also, all of the usual assumptions of regression will hold for path analysis. I won't work through all the math, but essentially what path analysis boils down to is that you can calculate all of the coefficients from a series of multiple regressions.
Path coefficients are equal to standardized regression coefficients.
This is essential . Path analysis absolutely requires this explicit statement of your statistical hypothesis. Reduce your data set down so that there are no missing values for any subset of the data that will be included in the path. Depending on the circumstances, you may choose to use some substitution methods, but the key thing is that the regressions are all based on the same exact set of samples. You may not add and subtract samples from different portions.