As said, the first thing you want to do with any character you play with is familiarize yourself with the character's move list. Obviously there's the command training and combo training. Afterward I would say that you should watch Allan Paris's break down of Hayate as a character, which points out all of Hayate's key moves, strengths, and weaknesses.
In a nutshell I'd say that Hayate is a well rounded character. Slightly above average damage, good speed, good launchers, good hold and throw damage, and GREAT space control. He can be played at any range depending on how hot you want to play. If you want to stay in and be aggressive, it's possible because he's got a generally good level of speed with his 10i jab, 12i mid punch, 12i dragon punch (Kick), and 14i low. Using these, you can run smart pressure up close and probably still survive. Another tool up close is his special sidestep which has strong evasive properties.
As for mid range to long range. He has a special type of space control. Ayane controls space defensively, to where she can easily make it tough for you to go in on her. As soon as you make the mistake of even trying, she puts you to shame. Hayate is one character who can roughly combat that. Hayate's space control is somewhat more offensive than defensive. He has to make space himself by actually backing away manually with special movements like the korean backdash. Once he's there, he has multiple tools that can get him in from mid range. Most characters won't have great keep out moves for this, allowing him to run a great pressure game at all ranges.
He's also got great wall damage so that's reason to get acquainted with his guard breaks and knockbacks. More often than not, you'll be looking to these for damage than anything else.
Hope this gets you headed in a generally good direction.