The L-sit is the motherlode of core exercises, and requires a combination of strength, flexibility and control in your arms, shoulders, abs, back and legs. They're tough, and require some working up to, but they're oh so good for you. Image by Anthony Topper.
L-sits are done by pushing yourself off the floor or by supporting yourself on parallel bars (parallettes), rings or even two chairs. In a floor L-sit, you need to work extra hard to push yourself high enough off the floor and then contract the heck out of your muscles to hold your body up.
It all begins with teaching yourself to comfortably form that L-shape from the floor and holding it for long periods of time. You'll find that even these "easier" variations are challenging if you're not used to contracting your arms, shoulders, hip flexors and quads that hard. In fact, cramping might happen and is normal. Antranik recommends that you stretch your hip flexors after every practise session.
Keep working on the five exercise progressions that Antranik shows you in the link below, but don't expect any overnight miracles. It took Antranik four months to be able to hold his L-sit for two seconds.
Floor L-Sit Progression Tutorial [Antranik]