Assembling a frame with half-lap joints is actually one of the easier glueups you’ll ever have to do. The process starts by applying a thin film of glue on each face and the shoulders of the joints. Then it’s a matter of applying a series of clamps to draw the joint tight.
I always have a few clamping pads on hand to prevent marring the workpieces and help spread the clamping pressure. I use hardboard pads, as shown in the photo. First, clamp with light pressure across the joint to bring the faces together. Then apply clamps across the frame in both directions, close to the joints, to draw the shoulders tight. Finally, tighten down the first set of clamps.