The Dave's Redistricting App developers have developed an online User Guide to help you draw your map.
This page will help you get started. For a whole bunch of resources to answer more in-depth questions, go here.
Draw the Lines has also created a virtual class. The first half gives an overview of redistricting, and the second half does a demo of the Dave's Redistricting platform (starting around 31:30).
Note: mapping on the DRA platform works best on deskcomputers, laptops, and tablets. It does not work well on phones.