Though there are numerous fine sources out there that can show you how to knit and purl, there are a few points about the process I'd like to highlight.

In the knit stitch, the yarn is carried in the back of the work (that is, away from your body.) In the purl, your yarn is in front, towards your body. In order to successfully complete either a knit or purl stitch you much first make sure that your yarn starts out on the correct location; otherwise you're sunk.

Secondly, your working needle, that's the one in your right hand (even if you're left-handed) follows the same rule as your yarn. For the knit stitch it wants to move through the stitch on the needle and to the back. The purl to the front. When you execute this move in either knit or purl, you want your needles to end up in a cross with both needle points facing upwards. That means that for knit you'll be shoving the needle upwards through the stitch and towards the back. And for purl you'll shove downwards and towards the front.

When you wrap the yarn around your right needle (and right needle only), it is absolutely imperative that it be wrapped as follows: towards your body and then into the area where the cross meets. The wrap is where I find the most confusion is for adults. If you don't execute the wrap correctly, you will be twisting your stitches and they will be oriented incorrectly on your left needle.

Pulling the wrapped yarn through to the opposite side of the needle is tricky to do at first, it is pretty self-explanatory. So is pulling that old knit or purled stitch off the needle. And your done!

Now, look at what you've created: That old stitch that you used to shove your needle through is now a bump. It sits in the back of the work in knit and in the front in purl. This is VITAL information. VITAL VITAL VITAL and tomorrow I'll tell you why!