If your scarf is still on the needles, then carollovesyarn’s suggestion of adding a new ball in is the way to go. If it is finished and bound off, however, then you can try to “pick up” stitches along the bound off edge and go on from their. What this means is to draw up loops of yarn back onto needles by pulling through a stitch on the finished edge of your fabrick; if it is a bound off edge, you would pull a loop up through the chain looking edge (both loops to give it strength) and put them on your needles to knit. If that doesn’t make sense, take your scarf, look at the bound off edge, and find the chain on the edge. Imagine pulling yarn through the chain in a series of loops. This will create a seam, though.
As for afghans, you will need long needles, as mentioned, if you want to make it in one piece… The easiest way would probably be on long circular needles; I’m currently using a set of 36" circular needles to pick up stitches along a sweater edge to create a button band. You want the needles to be shorter than the legnth you will knit; let the stitches bunch on the cable connecting the needles.