You can start doing this stich after doing rows of the knit stitch; starting a new knitting piece is not necessary.
To start you have to put the point of the RH needle into the first stitch on the LH needle from top to bottom (with the knit stitch it's bottom to top). Hold the needles in an X with the RH needle in front.
Bring the LH needle over the top and to the front of the RH needle.
Slide the stitch off the LH needle and tighten the yarn a little. Don't pull too much because it will be super hard to do the next row. See it's simple! Just like with the knit stitch you have to practice this one definitely. The yarn should still be in the front of the work after each purl stitch. Practice this stitch for a few rows or until you get pretty good at it so that you can be ready for the next lesson!! If you have any questions about this or any other stuff on the site leave a comment on the post and I'll get back to you on that.
Happy knitting :)
Ps. These aren't my pictures because I was having a lot of trouble with my camera (that's why I haven't posted anything in a long time) so I used Google images to find them.