When the pattern says to knit 18sts and then join another ball of yarn and knit the next 18sts it means that you'll be knitting two separate pieces at the same time, each with its own ball of yarn, each with a single strand of yarn.
So to do this, knit 18sts with the yarn you have been using all along, drop that strand of yarn and forget it for the moment. Pick up a new end of yarn and knit the next 18sts. Turn to do the next row and you'll see that you have the working strand of yarn right there at the end of the needle and you also have another strand hanging off the piece halfway down the needle. Pick up your working yarn and knit 18sts up to that hanging strand of yarn, drop the working yarn, pick up the hanging strand to knit the next 18sts. As you continue in this way to knit the rows, you'll see that a slit is forming where you drop one strand and pick up the other.