The second stitch on the needle in is the second color. This is the first stitch of the second side of your knitting, though it looks like it's all one "side" right now.
Bring both strands of yarn to the front and purl this stitch with the corresponding color (in this case gray). Only between the first and second stitches should you twist your yarns before forming the stitch. This hooks the two layers together and makes it so you're not knitting two separate pieces of knitting at the same time!
By purling on this side of the work, you're actually making the second layer Stockinette Stitch, too, because the knit side will face out as you continue to work.
Now just move both yarns to the back and knit the next stitch with the first color, bring the yarns forward and purl the next stitch with the second color and so on across the row.