For some projects, you will need to pick up stitches along either a horizontal edge (the cast-on or bound-/cast-off edge of your knitting), or a vertical edge (the edges of your rows of knitting).
ALONG A ROW-END EDGE
With the right side of the knitting facing you, insert a knitting needle from the front to back between the first and second stitches of the first row. Wind the yarn around the needle and pull through a loop to form the new stitch. Normally you have more gaps between rows than stitches you need to pick up and knit. To make sure your picking up is even, you will have to miss a gap every few rows.
ALONG A CAST-ON OR BOUND- (CAST-) OFF EDGE
This is worked in the same way as picking up stitches along a vertical edge, except that you will work through the cast-on stitches rather than the gaps between rows.
You will normally have the same number of stitches to pick up and knit as there are existing stitches.
For more knitting techniques and projects, check out Super Chunky Knits by Lauren Aston.