Weaving in the end of your work stops it from unraveling and can be completely invisible if done neatly. To start with I weave in along the back of the work in the opposite direction that I was knitting. You want to mimic the path of the stitch so that it is as invisible as possible.
One of the knitters, Kathy, from one of my KALs says: "work the tails from a smile into the frown in row above, then follow that frown around down into the smile of the row below" which sounds like a great way of remembering it!
Here is a visual of that in action:
Up through 'smile' on top row.
Follow 'frown' on left and into row below to the right.
Now follow through to the next stitch and go back up to the last top stitch.
Then just continue to work that across several stitches
.
When you've done that for a few stitches then pull the tail down diagonally and cut it with a little left. It sometimes helps to open the very end out so that it's less likely to pop out from your work. I sometimes wait until after a shawl is blocked to cut tails as I find aggressive blocking makes them very likely to come out again.
