My mom has had one of these as long as I can remember and asked me to make one for my sister and her family. In the process of making one, I used some scrap wood and ended up with three of them. It is a great way to use scrap wood and end up with something worthwhile.
Step 1: Gather Materials/Tools
5/16" or similar dowel
1x4" or other scrap material
Table saw with miter gauge
5/32" drill bit (or bit slightly larger than lollipop sticks)
5/16" drill bit to match center dowel
Step 2: Rip Scrap into square material
Rip your scrap material into equal dimensions. Ie: if your material is 3/4", rip it to 3/4" x 3/4". The lengths can vary because you will need various lengths to build the tree. You will need one piece for the base that is double this dimension or 1-1/2" x 3/4". If you miss that and cut all of your scrap, it just means you'll have to glue feet on the last row.
Step 3: Setup to drill center holes
Setup a stop on your drill press to drill as close to the center of each of the pieces as you can. When setting it up, drill a test hole, then flip the piece 180 degrees to see if the hole is within 1/16" of center.
Step 4: Drill Center Holes
Now drill the holes all the way through ALL of the pieces including the one that is 1-1/2" x 3/4".
Step 5: Trim Center Dowel and thread on drilled pieces
Now cut your center dowel about 1/4"-1/2" over the length of your tree. The bottom pieces in this picture are the ones to be cut. Your dowel should fit snugly into the freshly drilled holes. Too tight and too loose are both not going to work well. Sand your down if it is too tight.
When threading the pieces on, try to build something that looks like the tree your are expecting to end up with. Shorter pieces should be a the top. And do not forget the double-wide piece at the bottom.