Speaking as a new-ish diver (been certified for 9 years, but only just reached the 100 dives mark, 40 of them in the past 12 months):
1. Bouyancy - get the weight right, get comfortable, get to know your gear.
2. Relax and slow down - minimize excess movement, become aware of your surroundings.
3. Minimize task loading. Get used to diving, THEN bring that camera.
4. Situational awareness - depth, air consumption, position in the water, distance from the reef, location of your buddy
It's kind of like driving a car: when you first learn to drive, you're so busy with the mechanics of driving that your situational awareness is mediocre at best. When you don't have to think so hard about it, your focus can shift outwards and you can take in the big picture. A lot of it can simply be 'solved' by diving more often. The 'click' for me came when we started doing proper diving holidays instead of the odd '2 tank boat dive' crammed in the middle of a holiday. Getting our own gear also changed things for the better, since you spend some time figuring out what it is you want, and how you like it, and can get comfortable with it instead of fiddling around with rental stuff that is almost the same but just a bit different from the last rental stuff you had a year back...