Here's a picture of the topside of a 36" drogue chute.
The chute material is 1.9 ounce per yard rip stop nylon. The edge trim around the circumference of the chute is a product called Wide Single Fold Bias Tape made by Wrights, the product number is PC06. It's thin enough to fold over the edge and follow the contour of the circular fabric of the chute, but still goes a long way in protecting and reinforcing the edge. I use 7/8" wide nylon tape to reinforce in a cross between 4 of the grommets. The same nylon tape was folded over the edge of the chute to reinforce the other 4 grommets. I sewed at least 3 stitches on each length of nylon tape.
Here is the inside of the same chute.
I use a hot nail to melt a hole through the rip stop chute material and the reinforcing nylon tape. This hole is for the grommet. Grommet kits can be found at most hardware stores and home improvement centers for under $10.
The shroud lines are 1/8" braided nylon, the length of each shroud line is 1.1 times the diameter of the chute, since I use one continuous length of cord for a pair of shroud lines, I cut the cord at 2.2 times the diameter. I like the heavier nylon even on small chutes because it is less likely to tangle. The shroud lines are tied to each grommet using a bowline knot, each shroud line attaches to the grommet next to it, as opposed to crossing over the chute to its opposing grommet. All the shroud lines are gathered in a bunch at the start of the parachute and extended out to the end to find the exact center of each shroud line. Then I gather them together and tie a simple overhand knot to make a loop in the end of the shroud lines.
Here is a 10' diameter chute made for the Defiance rocket. It was a challenge holding this chute in the wind and taking a picture of it at the same time!