Shoulder presh.
For standard half-guard, I like to get head and arm*, turn the free leg almost perpendicular to my opponent**, get the arm which is under the head real deep and apply sufficient shoulder pressure to turn the head. Grab pants***, push down on his legs, wiggle wiggle, push push. With the pressure you are putting down with your shoulder, he will be unable to resist you forever. Slide into three-quarter mount when you get your leg free enough.
* there's a gi hack here wherein you feed your opponents lapel under the shoulder but I don't find it helps too much compared to the kind of shoulder pressure that works no-gi.
** getting your free leg perpendicular to your opponent will probably require you to lock out your trapped leg with your foot perpendicular to him ...this will help you once you get to the wiggle and push stage.
*** assuming gi. In no-gi, you probably won't need to, he's probably wearing short and his legs are probably dripping in his own grease
Other tips:
You must deny the double underhooks or you're in deep trouble. If he gets an underhook on the far-side, consider using a whizzer?
With your free leg, avoid putting your knee on the ground, have 'active toes'
Improve your half-guard game and pay attention to what people are doing that is beating you!!
Sometimes when my opponent tries to pummel for the underhook you can threaten a kimura.
One white belt to another, hope it helps.