A sew-on press stud has holes around each half for stitches. Reattach the loose half through those holes after checking that the two pieces still snap together. If the stud is crimped through the cloth and has no sewing holes, use the correct replacement method for that type or take it to an alterations service.
Check the mating halves before sewing
Press the detached half into its mate while holding both in your hands. It should close and release without unusual force. If either half is bent, cracked or loose even when snapped shut, use a matching pair. Check the fabric where the stud came off for torn fibres. A new set of stitches needs sound cloth or a repaired backing to hold.
Mark the position with the plackets aligned
Lay the garment flat and line up the overlap as it sits when worn. Use the old thread marks as a guide. A removable chalk dot on the receiving spot can help you check alignment. Confirm which way the working face points; when closed, the two faces should meet without twisting the fabric. Baste or hold the loose half at that point before stitching.
Sew around the holes
Anchor matching thread where the stud will cover the knot. Work small stitches through each sewing hole into the intended layer of fabric. Try to keep the front clear if the original stud was concealed. Use enough passes for each hole to hold without letting thread cross the raised centre or interfere with the release. Secure the end under the edge of the stud.
Open the stud by holding the fabric close to it
Test the closure several times while holding the plackets near the fastener. It should meet squarely and release without pulling the garment sideways. If the cloth puckers before the stud lines up, undo the stitches and adjust the position. If the two halves close well off the garment but not when sewn on, check their alignment before replacing the hardware.