Picking up stitches is a way to add to a piece that has been completed. To pick up a stitch:
Slide one needle into an existing stitch
Slide your other needle underneath, into the stitch as to knit
Pull the stitch through as in in knitting
You now have a new stitch on your needle
Pick up the next stitch.
Note: When picking up stitches you do not always have to pick up every stitch (your pattern will tell how how many to pick up).
You do not have to pick up stitches on the same row. This allows you to start a new part of your knitting (a collar, for instance, which would be joined in the round to several rows) which is very firmly anchored in the other piece.