When crocheting with 2 strands of yarn and changing colors what do you do with the dropped strands?

If I was crocheting with two strands of yarn and switching between the two, I would think about laying the unused strand over the top of the row below and just crochet my next stitch as usual. That is, if I were switching yarns in a single row. If I were switching yarns on different rows, I would just bring the unused yarn up on one side, by crocheting around it at the last stitch of the row.

Personally, I've not tried it, but those would be my suggestions. Bringing a yarn "along" and crocheting it in the row below is done in Tapestry Crochet (best know patternmaker: Carol Ventura). There is a different "process" with Tapestry Crochet, as you don't turn your work, and you use single crochet (sc), only.