Rayleigh Alpine handle bar assembly
On the other side of the steerer (stem quill) you should have a bolt (most likely with Allen recess) - unscrew this bolt slightly to the wedge (the part that resides on the thread of the bolt) moves away from the steerer. They become more aligned allowing to drive them down the head tube (actually into the fork).

Then tighten the bolt making sure that the handlebars are perpendicular to the weel. The more you tighten the bolt the more the wedge gets stuck in the fork tube. To remove the quill you first unscrew the bolt and then give it a gently tap with a hammer to unseize the wedge.

See the cross-section:



All of this under the assumption that the diameters of the stem quill and the headset correspond with each other.