Sempervivums are commonly known as Hens and Chicks. The mother plant (hen)during the growing season will give off offsets (chicks) that one can see tucked under her lower leaves or on the end of a stolon depending on the cultivar. Generally one doesn't need to do anything manually to propagate them except to wait for them to put out offsets (clones of the mother plant) which occurs usually in Spring/Summer.
Some members have found success in propagation using the individual leaves by laying them on damp soil and waiting for roots to appear.
Ellen, your semp appears to have been growing in cramped conditions? The growing center of your semp is not pointing straight up. What happened? Looking at your first photo: Is the center elongating a little? If so, it may be putting out a flowering bloom stalk?
