I had never done it before but the pattern you gave has good directions, and it works. I'll try to explain further.
The first thing you do is a M1R. There is a link to a video showing this increase HERE.
Look on the left as you scroll down for "M1R" it also says "I think of this as "M1B". You pick up the strand running between the stitches on the right and left needles using the left needle and approaching from behind. Once the strand is over the left needle knit it from the front (like you'd normally knit). Now you have increased a stitch and that stitch is on the right needle. Slip it directly back to the left needle, no twisting or anything.
*Now you are ready for the next part. You are going to be working with the stitch you slipped back to the left needle and the stitch next to it. Put your right needle behind the left needle and skipping the stitch you slipped, knit into the back loop of the stitch next to the slipped stitch. (Be sure when you knit into the back loop of that 2nd stitch that you go over, not under the working yarn that is attached to the stitch at the tip of the left needle.) Do the whole process of knitting that stitch through the back loop, until you get to the slide the stitch off part. Don't do that. (If you don't know how to k tbl click HERE. This is a page from the glossary on this site. Scroll down to "k tbl aka K1 tbl, K1b". There is a video link to how to do it there.)
Now bring the right hand needle to the front of the left needle and knit into the first stitch (the one you skipped) in the normal place. After you knit that stitch let both the stitch loops you have been working into slip off the left needle. You now have 2 new stitches on the right hand needle.
Now slip the stitch closest to the tip of the right hand needle back to the left needle (the working yarn will be attached to it). Now go back to the * and repeat.
The short version is to begin with a M1R, slip the increased stitch back to the left needle. * Knit the second stitch tbl, then the first stitch tfl, slip the stitch at the end of the right needle back to the left needle and repeat from the *.
Hint: Pay close attention and try to get in the habit of not stopping until you get to a spot where you can clearly see what the next step is. For me it was easiest to stop right after I slipped the stitch back to the left needle so that the working yarn was coming from the stitch at the tip of the left needle, and I was ready to repeat from the *.
I hope this helps you.