Pre-treating

Pre-shrink by machine washing gentle with cold water, low or no spin and air dry.
While eyelets are not terribly fragile, it is not a good idea to put them in the dryer as the embroidery thread might shrink at a different rate than the fabric itself.
Know your washing machine! As a rule, front loading machines are more gentle on fabrics than top loading machines. Making a test is a good idea.
I took 4 different eyelets from our collection and machine washed gentle and air dried. Laundering caused a bit of puckering, but pressing smoothed things out.
Each fabric shrank, so do not skip this step.
The plus: eyelets became a bit softer and shrinking resulted in a bit of stretch on the cross grain. This will vary from fabric to fabric depending on the holes.

Sewing

Stitch with a sharp #12/80 needle. If your fabric is very fine, use a smaller needle and fine gauge thread.
Keep seam finishes simple and flat. A simple pinked or serged seam is ideal as you want the seam to be barely visible.
Make test samples on scraps before stitching up your garment to determine the best needle, thread and stitch length.
No interfacing needed
Machine stitched hems work well as the stitching disappears into the embroidery.

Cotton Eyelets