the screenshots are to show how this looks and are meant solely as an example.

all pieces rotated (right click on the piece to rotate that piece)
so that the two light sides are at the top and at the right
with the brightest side at the right side
and the two dark (shadow) sides are at the bottom and at the left

update 23 feb 2023:
I see that the brightest side is now at the top edge of each piece
and the less bright side is at the left edge of each piece
and the darkest side is now at the right edge of each piece
and the less dark side is now at the bottom edge of each piece

update 12 april 2023:
the brightest side is at the right once again, in other words the light comes from the right

update 11 may 2025:
the two bright sides are now at the left and the top edge with the brighest side at the top
the two dark sides are now at the right and the bottom

the shape that's needed for that open place in the puzzle and the shape of the piece need to match
look also at the color and the color patterns

first, I solve the border: place together
the pieces that belong to the top border
the pieces that belong to the bottom border
the border pieces with one protrusion to the left and no protrusion to the right
the border pieces with no protrusion to the left and no protrusion to the right
the border pieces with one protrusion to the left and one protrusion to the right
the border pieces with no protrusion to the left and one protrusion to the right

the pieces that belong to the left border
the pieces that belong to the right border
the border pieces with one protrusion to the top and no protrusion to the bottom
the border pieces with no protrusion to the top and no protrusion to the bottom
the border pieces with one protrusion to the top and one protrusion to the bottom
the border pieces with no protrusion to the top and one protrusion to the bottom
example


solve as much of the jigsaw puzzle as you can.

place all pieces with the same number of protrusions together in the same box below the puzzle area

for example:
all pieces with 0 protrusions in the first box

.
all pieces with 1 protrusion in the second box

.
all pieces with 2 protrusions in the third box

.
all pieces with 3 protrusions in the fourth box

.
all pieces with 4 protrusions in the fifth box

.
the pieces with 0 protrusions are ready (because all sides have no potrusions)
the pieces with 4 protrusions are ready (because all sides have one potrusion)
.
sort / group all pieces with 1 protrusion with the same orientation together
meaning
the pieces with that protrusion at the top are together
the pieces with that protrusion at the right are together
the pieces with that protrusion at the bottom are together
the pieces with that protrusion at the left are together

the same with all the pieces with more protrusions

then you can look at the puzzle area to know which piece with this number of protrusions in this orientation (the shape that's needed for that place and the shape of the piece need to match) you need for that place, by placing together the pieces with the same number of protrusions in the same orientation you have reduced the number of pieces you have to look at to find a matching piece. This is extra work but in the end this saves even more time than without this.
I can put more pieces in place when I look at a place and find the piece for this place (adding to the pieces already in place) than I have a piece and look where to place it.