Slipping stitches is about as simple a technique as you will find in knitting, yet it can be used to create an unlimited number of color and texture patterns. The basic maneuver simple: put the tip of the right needle into the first stitch on the left needle. Slide (slip) the stitch off of the left needle without working it. It is now sitting on the right needle and you are ready to work the next stitch on the left needle. Easy! But there are a couple of fundamentals to be aware of.
Knitwise vs. Purlwise
There are two different ways you can slip that unworked stitch over. You can insert your right needle as if you were going to knit it.
This is called slipping "knitwise" (kwise) or "as if to knit". Slipping knitwise is often used as part of decreases (eg. SSK), because it turns the stitch in preparation for the rest of the decrease. However, when slip stitches are used as the basis for pattern stitches, they are most usually slipped purlwise (or "as if to purl"), as in the picture below.
This is because you generally do not want to turn the stitch (which would result in a twisted slipped stitch once it is worked on the next row or rows up).
Good directions will tell you whether to slip knitwise or purlwise. This information may be given as part of the row directions, for example "*K3, sl1 pwise; rep from *". Or there may simply be a statement at the beginning of the directions that says "All slipped stitches are to be slipped as if to purl (or purlwise)."
If the directions for a pattern stitch do not specify, assume that the stitch is to be slipped purlwise.
wyif vs. wyib
"wyif" means "with yarn in front" and "wyib" means "with yarn in back". These terms describe the placement of your working yarn as you slip the stitch. It is important to realize that the terms have nothing at all to do with the "right" and "wrong" sides of the fabric you are creating. They refer exclusively to the placement of the working yarn in relation to you as your work the pattern row.
"With yarn in back" means that the working yarn is at the far side of your work (the side away from you) as you slip the stitch. "With yarn in front" means that the working yarn is at the near side of your work (the side closest to you). This may or may not involve moving the yarn from front to back before and after slipping the stitch.
If I am working on a knit row and the directions tell me to sl1 wyib (slip 1 with yarn in back), I do not need to do anything with the working yarn. It is already at the far side of the work in position to knit. (You can see the position in the pictures above.)
If, however, I am working on a knit row and the directions say sl1 wyif (slip 1 with yarn in front), I will need to move the working yarn towards me between the needle tips and hold it there as I slip the stitch,
and then I move it back away from me between the needle tips after I have slipped the stitch.
This has brought the yarn back into position for me to knit the next stitch. (If you look closely, you will see that it has left a little "bar" of yarn in front of the slipped stitch.) Good pattern stitch directions will tell you whether to slip wyif or wyib.