What hyperactive said is very close but one important part is wrong.
Put the RHN (right hand needle) into the first stitch purl wise, but don't do anything to that first stitch, just go through it. Go into the second stitch in the normal way and knit it to the point where you have pulled up a new stitch loop, but don't take anything off the LHN (left hand needle) yet. Now you have one st loop on the RHN and a strand from going through the first stitch, you also have 2 loops going over the LHN. Don't take the RHN out of the stitches (this is where she was off) or everything you've done comes undone. Instead you must rotate the RHN tip around until it is behind the LHN and put the tip of the RHN into the first stitch on the LHN right to left, and knit it there. Now you take the whole works off the LHN, and you have 3 stitch loops on the RHN. So this is an increase. You change 2 stitches into 3 stitches. You will probably do something on the next row to get the stitch count back down.
This explanation covered how to do the knit through the back loop that you wondered about.
This is kind of tricky, but not too bad if you knit loose enough. If you knit real tight I think it will be very difficult.
hyperactive, you did a good job for not having the yarn and needles in hand.