Don't worry about the number of steps in this; it's not complicated, I'm just trying to be thorough.
Step 1: Materials
1) Paper - plain ol' printer paper should do just fine.
2) A Writing Implement - something that can leave light marks. I used a 0.5mm pencil.
3) A Cutting Implement - scissors should work fine, but I used an X-Acto knife and a cutting mat to go with it.
4) Glue - I used Tacky Glue, though just about anything for paper should work.
5) Tape (optional) - I used some masking tape in some later steps to check how things fit together before gluing.
Step 2: The Template
Step 3: Add the Edge
Step 4: Cut Out the First Layer
In this case, I cut it too shallow... but we can fix that later.
Step 5: Cut Out the Additional Layers
It may not look like it, but the random edges can make a difference... at least, I think so.
Step 6: Check the Layers Before Gluing
So for this reason, I suggest a "dry fit" before gluing anything in place. It's better to spot your error with tape that's relatively easy to remove than with semi-permanent glue.
The photo fails to illustrate this, but I cut the wedges in the cones at about 30°. After checking with the tape, I went with something near 90°.
Step 7: Glue the Layers
As you can see, there's a seam on each one that is a bit of an eyesore. As I've yet to find a way to eliminate those from paper models, it's probably best to hide those by turning them towards another feature in whatever display you make these for.
The angles don't have to be uniform; If you look closely, you'll see the smallest one is sharper than the others.
Step 8: Start on the Trunk
This part is just a short, wide cylinder that props up a couple layers. But it's important to get the spacing right; just a little bit should do, but you want it to remain hidden under the branch layers.
I suppose a good formula would be to make it's height about 1/3 the length of the seam on the layer it sits on.
Step 9: Glue the Trunk to the First Layer
Also remember to align the seams at this point. You don't want a bunch of ugly seams radiating in every direction!
Step 10: Let the Glue Dry and Cut Out the Second Trunk
Step 11: Add the Last Trunk and Layer
Step 12: Results and Final Thoughts
Looking back, there's a lot you can do with this idea. You could use some fancier paper, add decorations, or use more layers (now that I think of it, I think my original run had 4 layers...)
And for reference, each square in the photo is 1".