Making Sense of Logistic Regression Coefficients

I would like to translate coefficients into a meaningful scoring of some type and maybe even derive the complete prediction formula that leads to the probablility prediction value.  It would be great if I could hand someone a formula and say "here's how this data mining model works, plug in some values and try it".  I'm not a statastician, so I'm looking for some fairly simple reference to help me.  Any suggestions?

I have a Logistic Regression implementation that uses demographics and historical data to predict future action based on about a half dozen input variables. 

I'm able to retrieve the data from the Content queries, but I'm having trouble trying to tie coefficients back to anything intuitive or useful to the business in determining if the model makes sense or not. 

A particular problem I' finding with coefficients is that frequently for a given input attribute influencing a "will" or "won't" outcome, coefficients for both outcomes are negative.   How can attributes have a negative influence on both the "will" and "won't" outcomes?  I wish they simply added up to 100% or were more intuitive in some way like the Support distributions are.  The Lift Chart looks good and empirically the model is definitely working.