A shank button has a loop on the back. Sew through that loop and the fabric beneath, keeping the button aligned with its hole. Before replacing a school blazer button, check whether a spare from the school uniform shop is needed to match the colour, crest or design.
Inspect the attachment point
Lay the blazer flat and close the remaining buttons. Use the old stitching marks and the matching buttonhole to locate the centre of the new button. Examine the cloth around it. If the first button pulled through the blazer fabric, a hidden backing or a tailor’s repair may be needed. Look inside at the same point to see how the lining is attached and whether the original sewing went through to it.
Check the shank and face direction
Make sure the replacement passes through the buttonhole without force. On a crested button, hold it against the blazer in the direction it will sit when fastened. Check the loop is sound and the position will not make the button turn sideways or trap the lapel. A shank already provides clearance; you generally do not need to build a long thread stem underneath.
Sew into the intended layer
Use thread and a needle suitable for the blazer cloth. Anchor the thread, then pass through the loop and into the outer fabric several times while keeping the button face in position. If the original construction allows it, keep the free lining clear of your stitches so it can move independently. Do not open a lined jacket just to reach the spot if you cannot close the lining neatly. Secure the thread near the base of the button.
Close the blazer and inspect the drape
Fasten the new button and the ones beside it. The front edges should meet without pulling or rotating the button face. Check inside for a lining pucker and test the fastening several times. If the cloth deforms under a light pull, stop and have the attachment reinforced before wearing the blazer.