How to Do a Garter Stitch (Version 1)
Step1
What your garter-stitch coaster will look like
Set up your stitches.
Cast on three stitches. Knit one row. On the next row (this will be your right side) make one stitch between each knit stitch for a total of five stitches. Knit the wrong side to the end.
Step2
The increase half
For every right-side row: knit 1, make 1, knit to the last stitch of the row, make 1 and knit 1. Each right side row will increase your stitch count by two stitches. Knit across every wrong side row. Repeat this until you have reached 23 stitches or your coaster is as wide as you want it. Then knit two rows (one right side, one wrong) with no increases.
Step3
The decrease half
For every right-side row: knit 1, slip 1, knit 1, pass slipped stitch over (psso), knit to the last three stitches, knit 2 together (k2tog) and knit 1. Continue to knit all the wrong side rows and decrease on the right side until you're down to five stitches, ending on a wrong-side row.
Step4
Finishing up.
For the next row slip the first stitch, knit the second and psso. Knit 1 and then k2tog. On the wrong side, k2tog, knit 1, and then bind off those two stitches by passing the one over the other and pulling the tail of yarn through the final loop. Weave in your ends and you're done!
How to Do a Stockinette Stitch (Version 2)
Step1
The increases and decreases on the stockinette coaster are more obvious, but in a good way.
The beginning
Cast on two stitches. Knit into the front and back of the first stitch and knit the second stitch for a right side of three stitches. Purl the next row and all wrong-side rows. For the next right side row make one stitch between each knit stitch and purl the wrong side.
Step2
Increase to 24 stitches, ending on a wrong-side row.
Increase three stitches on each right-side row by doing a make 1 after the first stitch and before the last. For the center increase, alternate a make 1 between the two center stitches for rows that start with an even number of stitches and knit into the front and back of the center stitch for rows that start with an odd number of stitches. Once you've reached 24 stitches, knit a row without any increases and purl the reverse.
Step3
Decrease to six stitches, ending on a wrong-side row.
After the first stitch of each right-side row, slip 1, knit 1 and pass the slipped stitch over (psso). At the center of each row, alternate this decrease with a knit-2-together (k2tog), knit to the last three stitches, k2tog and knit 1 to finish the row. Continue to purl the wrong-side rows.
Step4
Complete the final decreases and bind off.
Knit 1, slip 1, psso then k2tog twice. On the wrong side, purl two together, purl 1 and pass the first stitch over the second, pulling the tail of yarn through and weave in your ends. Since stockinette stitch tends to curl, you will need to block the coaster before using it.