This comes from Weaving for Beginners on 115. It’s quick and does the job nicely.
How to change wefts
I like to tuck in the old weft about ½” into the next shed, snugging it up against the selvedge and pulling the tail out of the shed to let it
lie on top of the cloth. The shed stays open, ready for the new weft. I leave the new weft’s tail, which is about 1″ long, dangling outside the selvedge and cut it off later. See Figure 272. Other ways to change wefts for other yarns are given on page 131.