A simple yarnover "yo" looks like this:
All you are doing is draw the yarn over the needle and then knit the next stitch on your left needle. You will then have one additional stitch on your right needle, but it will be loose and not look like the other stitches. That's good! That's what you want.
From the purl side, your yarnover looks like this:
The 'yarnover' stitch is still on the left needle. Note how loose it looks. New knitters have a tendency to let this "stitch" slide off the needles because it looks wrong. Don't do it! Purl it into place. From there on it will be anchored to the needle, just like your 'regular' stitches.
The picture below shows how you knit a "ssk" or slip-slip-knit stitch. First you slip two stitches from your left needle onto your right needle, one at a time as if you are knitting them. Then take the tip of your left needle and insert into those two stitches as noted below. Bring your yarn around as you normally would to knit, and knit these two stitches together.This creates a left-slanting decrease.
To do what is called a "psso", understand that this term is used in conjunction with other actions, such as "sl 1" or "k2tog". Pictured below I am sliding a stitch from the left needle onto the right needle. Then I will knit the next two stitches together.
This final picture shows me doing a "psso" or passing the slipped stitch over the one stitch which I created from knitting two together. Again, doing a "psso" will give you a left-slanting decrease in your work.
When you knit-two-together, (k2tog) you get a right-slanting decrease in your work. When knitting lace or open-weave designs, these slants become important to your designs. They are so easy to do, but look terrifically difficult, so don't tell anyone! It's just another knitting secret!
Practice these simple lace stitches and then try out the 'feather and fan' stitch to create a scarf or practice block. It's all about keeping track of your rows, and doing exactly what each row says to do. Don't always try to keep track of your stitches, because when increasing and decreasing in a pattern, you don't always have the exact stitch number you cast on with, and that can be confusing. So if, for example, you cast on 47 stitches and in Row 12 you now have 53 stitches, that is probably exactly what the pattern is calling for. So, don't get nervous if it seems wrong. As long as you follow each row carefully, your pattern will work out! Another secret!