When I started identifying species last year, I turned to Woody Plants in Winter by Earl L. Core and Nelle P. Ammons(who also illustrated the pen and ink drawings.) I had a hard time learning the identifying characteristics and then applying them to specimens.
I recently picked up the book again and am now getting comfortable. Here are a few things I've been studying. I'll use the Tree of Heaven as an example.
This branch displays a leaf scar, bundle scars, and lenticels. The leaf scar follows the shape of the petiole (leaf stem) where it joins the branch. For comparison, we can see the attached petiole in the second photo. Within the leaf scar we find the bundle scars. These are the channels through which pass the vascular bundles carrying nutrients from the branch to the leaf. The lenticels, those little lightly colored dots on the branch, admit air to the living tissues beneath.
Sizez and shapes of leaf scars, bundle scar location and count, and lenticel presence, size and shape are very useful characteristics for making an identification when leaves, flowers, or fruit are not present.
There is one gotcha with this identification practice. We can see here that the Tree of Heaven has a compound leaf and will leave the same scars as a single leaf. Single versus compound leafing is a very usefual property in identification and is something we can't count on in winter.
There! That's a bit of what I'm digesting. :-)