The relationship of club head path to club face angle at impact determines the shape of your ball flight (i.e., left curve, right curve, or dead straight), while it's mostly club face angle at impact that determines your ball's starting direction. This is all based on the proven "new" ball flight laws (9 potential shapes) and D-Plane theory. Stated simply, the "old" ball flight laws taught that the starting direction of the ball flight was determined by the path, while the face pointed at where the ball flight would finish. The "new" laws state the opposite.
Problem: You usually hit a draw but today you're hitting fades and pull-hooks that are not terrible but are leaving you in the rough. You can't figure out how to get your draw back. You strengthen your grip, close your stance, feel like you're swinging right, rotate your left forearm, and nothing you try is really bringing your nice draw back. Should you be trying to adjust your club path or club face angle? For most golfers who have hit nice draws in the past, they should be trying to fix their path. It's likely that MOST golfers should be scrutinizing their path, especially if their ball is starting on the right line. Because the face and path have a relationship that's actually reasonably fixed with a good grip, adjusting the path will often adjust the face angle automatically, without doing anything different. This is why better players who often "lose" their draw start hitting pull-hooks; the face and path still have the same relationship, but the path is now outside-in. The entire club face-club path relationship shifted left.
No matter what the shape of your backswing, it's the first six to twelve (6-12) inches from the top of the downswing that programs what path the clubhead will take back to the ball. So it's the initial drop of the hands and handle that need your attention, though it's true there are many ways to influence how a particular path witll occur.
When the club head is still above the hands during the transition and downswing, the butt end of the handle is automatically pointing at the path the club head will take into the ball at impact. The club head will always follow where the end of the handle is pointing at this point during the downswing. Try this drill: Go to the top of your backswing and then start down but stop after about 6-12 inches; your hands should be somewhere vertically between your sternum and your waist. Where is the butt end of the club pointing? Chances are it's pointing at the target line or even left of it already. This means you're already over-the-top and swinging outside-in. This may be what you want if you're a skilled player and trying to hit a fade, but that's not the case for most of us. If the butt end of the handle is pointing out to the right, you can probably expect one of the following ball flights: 1) push; 2) push-draw; 3) hook; 4) push-slice. Which of these you see depends entirely on the face angle relative to the amount of inside-out swing path you're using at impact. Could you see a pull-hook with an inside-out swing? The new ball flight laws say yes, but this is a highly improbable occurence, as most golfers--even beginners--would not have the impulse to swing outside 45 degrees with a club face closed the other way (this would make me feel as if I was trying to hit the golf ball with toe edge of the club).
How do you ensure you have an inside path back to the ball? First, ensure you make a good, compact, connected backswing, where you keep both elbows close together--the same distance between the elbows that you started with at address. This may not be a problem for you, but I personally fight a flying right elbow. The right elbow must be able to drop back in front of the body unhindered by crashing into the right side, and keeping good external rotation in the right humerus is crucial. Next, keep your attention on where the butt end of the club handle is pointing during the first 6-12 inches of the downswing (i.e., while the hands and handle are dropping); you must keep it pointing out to the right or towards the left-rear quadrant of the golf ball during this period of the downswing. The only way to do this, you'll find, is to keep your back facing the target just a touch longer during this period, so thinking of where the handle end is pointing helps you automate this move. This keeps you from opening your shoulders too soon, which is a major cause of swinging outside-in.
There are numerous other swing thoughts and feels you can use to achieve an inside-out delivery. I've already alluded to one of them: Keep your back closed while your hands begin to drop. You can also focus on the club head end, ensuring it falls behind you somewhat before arcing down towards the ball.