Handling a basketball well does not happen overnight or over a year's time. It took me at least five to seven years to reach the point where I was a good ball handler and could protect the ball in difficult situations.
When I was a rookie in 1972, and even now, I liked Nate Archibald, particularly the way he dribbles with his head up. Too many players have to look at the ball when they dribble, which slows them and often makes them unable to see open teammates. Since advancing the ball is the primary goal of a point guard, you are hurting your team if you don't keep your head up. Work on this by sitting in a chair and dribbling while looking straight ahead.
You'd be surprised how many players don't know how to use their hands and fingers while dribbling. Only the fingertips of your dribbling hand should touch the ball; they should be on top of the ball, almost like you are palming it (see photo). This calls for strong fingertips and forearms so do fingertip push-ups, working up to 10 or 15.
Protect the ball with your body and also with your off-arm. Don't push off with the off-arm, thoughs that's an offensive foul.
There are other things I look for in a point guard. Zones and double-teams can stop even the best dribbler, so you need to develop an effective outside shot to keep defenses honest.
You must play under control. Many players, myself included, have had to learn when to leave their feet off the dribble. If you leave too soon, you may not have a good shot or pass available, or you may charge.
Also, don't get too fancy. I see potentially good players trying for sensational plays and not sticking with the fundamentals of ball handling, and it lessens their effectiveness. I really curbed myself in the last three or four years, and I am a better player because of it.