The Half Guard is both a dangerous spot because your opponent already has passed one leg, however it is also a dynamic sweeping position for you as the bottom player. Just like when passing the Half Guard your first action should be pummeling for the Underhook. The underhook from bottom gives you leverage to be able to move your opponent up and create space.
Once the underhook is claimed immediately begin sitting up, using your underhook for leverage to lift your opponent closer to you. At the same time use your free elbow to post. From here take your outside leg and cross it over your opponents closest leg. Drag your bottom leg underneath so that it is now on the outside of your opponent and you are turned into them. This is known as switching from outside leg control to inside leg control. At this point your opponent may react. If they dont though you can finish the Single Leg by using your outside arm to grab your opponents far ankle first and the nearside arm to grab the far knee. Drive into your opponent, knocking them to the mat, and work towards maintaining Side Control.