How do I read the results of my eye exam to know how bad my vision really is?

Difficult. A problem is that the number you receive for your eyeglass prescription does not easily correlate with the snellen fraction (the one that says 20/20 or whatever). So for instance a +2.00 correction might see 20/40 uncorrected while a -2.00 (note the sign) correction might see 20/100 uncorrected. Ask your ophthalmologist how bad your vision is in a meaningful way if this is important.
Show what you have. Snellen acuity i.e. 20/20 lists how far you can see something compared to someone with normal vision. E.G. 20/40 means someone can see it at roughly 40 feet what you can see at 20 feet. (has to do with minutes of arc of letters).