I just knitted a vest on two needles in two colors. The directions say “using a flat seam for ribbing and a fine back-stitch seam for the remainder, join side seams and armbands.” What are these techniques, and how do I account for the two colors?
Mattress stitch will give you a nice flat seam for attaching the ribbing armbands. You can also use it for the remaining seams, but IMHO backstitching the shoulders creates a firmer seam that won’t stretch.
As for the two colors: if there are large sections of each color at the edges of each piece (wide stripes, for instance), match the sewing-up yarn to each section. For narrow stripes or a mixture of colors, use either color. If you do mattress stitch or backstitching carefully, the yarn you sew with won’t show on the outside.
Info on mattress stitch, backstitch, etc. are here about two-thirds of the way down the page – I always quite enjoy making up. 
Thank you for this. Can you describe mattress stitch and IMHO backstitching or tell me where I can learn what they are?
Hi, welcome to KH!
Amy has a video of the Mattress Stitch hereunder knitting tips, just scroll down to finishing 
Thank you, Zena.
Thank you!
I just sewed up my vest using the mattress stitch and it worked like magic! All the stripes line up and it looks professionally done. I am very excited and can’t wait to show my knitting friends.
Yay, you! Don’t you feel clever?