Often, Harry will offer her a handkerchief or a tissue if there is one available. He might also put his arm around her in a comforting gesture. In 'The Common Room Crisis' fanfic, he does just that and then stays with her, listening intently as she pours out her feelings. He is patient and understanding, which is in line with his character in the original books. He tries to make her laugh or at least smile by sharing a joke or a funny memory. This shows his deep friendship and care for Hermione.
She probably comforts him right away. Hermione is a very empathetic person. She might give him a big hug and let him cry on her shoulder.
Harry might immediately rush to her side and comfort her. He could put his arm around her and ask her what's wrong in a gentle voice.
Harry might be initially shocked. He's used to seeing Draco as this tough, arrogant Slytherin. But then, he could feel a bit of pity. He might approach Draco tentatively and ask what's wrong. Harry has a good heart, and despite their past differences, he wouldn't just leave Draco crying. He may even offer some words of comfort or a handkerchief if he has one.
Well, it could be that he's feeling the weight of his destiny. Harry has so much on his shoulders, like fighting Voldemort. Maybe he just had a particularly tough encounter with the Dark Arts or lost someone dear in the fight against the dark side. Another reason might be his feeling of isolation. Despite having friends, there are times when he feels alone in his battle.
She might be initially shocked. After all, Draco is usually seen as this tough Slytherin. But then she could feel sympathy. For instance, she might offer him a handkerchief without saying much at first.
One great fanfiction could be 'The Unspoken Pain' where Harry stumbles upon Hermione crying in the library. It delves into the stress she's under from all the studying and the looming threats in the wizarding world. Another is 'A Moment of Weakness' which shows a more personal side of Hermione, perhaps feeling left out by her friends, and Harry is there to comfort her.
Another great one is 'When Draco Saw Harry Cry'. This fanfiction focuses on the moment of discovery and how it changes the dynamic between them. It has some really heart - wrenching moments as Harry is dealing with his own issues and Draco has to decide how to respond.
Perhaps he's feeling isolated. Even though he has friends, he often has to face his battles alone in some ways. Ginny finding him crying could be a moment of vulnerability that she witnesses, and it might be related to his feeling of being alone in the fight against the dark forces.
Hermione would likely be a mix of disappointed and worried. Disappointed because Harry is usually responsible, and worried because she cares about him. So she'd probably try to figure out why he got drunk in the first place.
He might be initially startled. Snape is used to seeing Hermione as a strong - willed and confident student. So seeing her crying could catch him off - guard. But then he might quickly put on his usual cold facade and ask her curtly what's wrong.