The art of hitting out of a fairway bunker isn’t “picking it clean”. It just takes the ability to hit the ball first. This is the same skill that you need to hit the ball off the fairway. This idea of “picking it clean” actually causes amateurs to do some interesting things that actually cause more problems.
When an amateur gets in a fairway bunker and sees the lip that they have to get over and then try to pick it off the sand, they usually end up trying to help the ball up by falling back onto their trail foot and extending the lead wrist early in a scooping fashion. This almost always makes the player hit the sand first. This is the exact problem they were trying to avoid.
Instead, make a few key modifications and then hit like you would on the fairway. First, pick a lofted club that will get over the lip even if you hit it a little low. Don’t get too aggressive. This will help you resist the temptation of the fade away scoop. Second, play the ball slightly back in your stance and set your weight a little more on your lead foot. This will help you hit the ball first. From there swing normal, just like the fairway. Maybe don’t try to nuke it, but the less you over analyze and more you hit the ball first, you’ll be fine.