Choose the one that works best for you. Either method gives a neat, flat vent. The overlapping side along the vent edge can be stabilized with fusible interfacing. You may choose not to put it in the hem. Sewn-in interfacing can also be used.
Catch stitch it in place.
Before finishing the vent, lay the garment wrong side up on a table. Arrange the vent layers in the finished position. Trim the layers of the vent so they are even with lower edge of the garment. The mitered corner technique is neat in appearance, eliminates bulk in the vent area, and allows the hem and vent edge to be smooth. Unfold the fabric to see the pressed lines.