what part are you having trouble with ?
the way I see it is just a round wooden frame (rings), probably cut out
with the jig saw with internal vertical braces and the cedar shingles
cut with a tapered end and laid one on top of the other, shingle style.
I would not try to cover the whole thing "wrapped" in plywood.
just tack the shingles to the horizontal wood rings (spaced accordingly).
googling "conical shape roof" turns up a few examples.
I remember my father making a conical shaped lamp shade out of red cedar.
he processed a big piece of wood then shaved off 1/8" slices on his band saw.
since the birdhouse isn't all that big, you could figure out about how big
you want the roof to be and cut a whole bunch of vertical strips that are tapered
and staple them to the horizontal round frames.
since the roof would be "my" most challenging part, I would make it first.
then, build the "house" part under that.
shape a big piece of wood for the vertical "staves" (for the lack of a better word)
and slice them on your table or band saw.
and make all those itty-bitty shingles the same way.
(I keep forgetting this is a birdhouse - and not a full size gazebo).
making a prototype out of cardboard would be a good idea.
what size are you going to make the roof ?
(with my very elementary math skills, it looks to be about 24" at the base
and 18" tall).