Sirius would probably be very concerned. He might immediately ask her what's wrong and offer her a handkerchief to dry her tears. He has a bit of a wild side, but he also has a big heart, especially when it comes to those he cares about or sees as in need of help.
It could be that she's homesick. Even though she loves being at Hogwarts, sometimes she might miss her muggle family a great deal. Also, she might be crying because she's being bullied. There could be some students who are jealous of her intelligence and are giving her a hard time. In the fanfiction, Sirius finding her crying might lead to him becoming a sort of mentor or protector for her, helping her deal with whatever is making her sad.
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.
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.
Well, James is a loyal friend. So, when he discovers Sirius is abused, he would most probably drop everything else he is doing to focus on Sirius. He'd be angry, not just at the abusers but also at himself for not realizing it sooner. He'd make sure Sirius knew that he wasn't alone and that he had someone who would always be there for him. James might also encourage Sirius to learn self - defense magic more intensively so that he could protect himself in case the abusers tried to harm him again.
Often, it begins with Hermione trying to help Sirius deal with his post - Azkaban trauma. She uses her knowledge and compassion to reach out to him. As he heals, he starts to see her in a new light. Their relationship then grows as they start to understand each other better. The lemon parts usually are used to explore their more passionate and private moments, which are often written in a very tender and intense way, adding a new dimension to their relationship.
She might initially be defensive. Hermione is proud of her intelligence and actions, so she could start by trying to justify what she did. For example, she could say that she was only trying to help or that she had good intentions.
Sirius would likely be extremely angry. He already has a protective streak towards Harry. He might immediately confront those he suspects of the abuse, whether it's the Dursleys or others at Hogwarts. He would probably also try to remove Harry from the situation as quickly as possible.
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.
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.
Sirius might immediately rush to Harry and give him a big hug. He's like a father figure to Harry, so physical comfort would be his first instinct.