I have been instructed to use the colors in a palette (there are three) but that I can use tints.

So, what is a tint and how do I do it?

I probably need to ask the person who told me about tints - "What do you mean when you say tints?"

I thing she means that I can add white. Let's say I have a color - how do I add degrees of white? I have one technique where I duplicate a shape, put the dupe on top, and then make it white and adjust the transparency. Does that seem like I am accomplishing tinting? Any other suggestions about definition or method?

Traditionally to tint means to add white paint to your color and to shade means to add black. The concept does not have much meaning in digital media, because the rgb model does not recognize tints in any useful way. You can simulate tinting by using the HSV or HSL color pickers and varyng the V or L value without touching the other two, but this will get converted to RGB in the SVG file.
The final printing method will really influence how you go about this.

Thanks very much! I will use the HSL picker to get what I need.