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I started by measuring my bassinet. I don't know how much difference there might be between brands and styles, so I suggest that you measure yours before cutting any fabric.
There are 5 basic parts to the cover: bottom, long side, short side, band, and skirt. The bottom goes at the bottom of the bassinet, the mattress goes on top of it. The long and short sides are the interior sides of the bassinet. If your bassinet is rectangular, you have 2 long sides and 2 short sides. The band fits closely over the top outer edge of the bassinet. And the skirt is the rest of the outside, with the ruffle at the top and hem at the bottom.
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Here are the measurements of my fabric for each piece, with a 1/2 inch seam allowance. My bassinet is sightly oval shaped, and the vertical sides flare out a little, which is why I have rounded corners on the bottom piece and trapezoid shape on the short side pieces. The band is made from 2 strips that are 4.5x44 inches. The skirt is made from 3 pieces that are 26x44 inches (my fabric was 44 inches wide).
I started by sewing together the long and short sides. Then I sewed it to the bottom piece. This makes a little basket kind of shape. I sewed together the 2 band strips into a loop, then sewed that to the top of the side pieces.
I did the skirt last. I sewed the 26 inch sides together first. Then basted the top edge (for the ruffle). Make the ruffle, pin it to the band, and sew it in place. Last make the hem. I made mine about 24 inches from the band to the ground, and it doesn't quite touch the ground. If you want it to reach all the way to the ground, hem accordingly.
I hope that makes some sort of sense, I'm not good at making patterns or tutorials.