Start with a reference
Give colour as a Pantone TCX (textile) reference or a physical swatch. Screen colours are not reliable references because every screen shows colour differently.
Lab dips
For solid colours, the dye house dyes small fabric samples to your reference, usually in a few options. You approve one, and bulk is dyed to it. Approve under the same light (daylight D65 is common) each time.
Strike-offs
For prints and embroidery, a strike-off is a test of the artwork on the real fabric. It confirms colours, scale and quality before the garment is sampled.
Shade variation in bulk
Bulk fabric can vary slightly between dye lots. Agree a tolerance and ask that each garment is cut from a single lot so pieces within a style match.