L1:
Knit into stitch below on left needle.

You can see, to work this increase you just stick your needle right into the middle of the stitch on the row below and knit it. Remember though that the existing stitch on the left needle stays there!

L1b:
Knit into back (purl bump) of stitch below on left needle.

This increase works into the back of the stitch on the row below. From the photo you can see you reach your working needle back behind the next stitch on the left needle. Insert this needle from the top of that purl ‘bump’ and knit it. Remember again to leave the stitch on the needle (or you aren’t increasing a new stitch!).