Join yarn in crochet
Change yarn on the last pull-through of the old stitch so the next stitch starts in the new colour.
Work the technique
Work the current stitch until its final pull-through. Drop the old yarn, draw the new yarn through, leave tails and continue. Weave tails into the reverse-side fabric in different directions.
Try it on a sample
On a 15-sc sample, change colour on the final pull-through of stitch 15, then ch1 and turn with the new colour.
Check and recover
Joining in the middle of a tall stitch can show both colours. Keep a soft join; test woven tails by stretching the washed swatch before trimming.