What type of evidence is needed to prove harassment/bullying at the workplace?

First, you have to be aware that most harassment or bullying in the workplace is perfectly legal: as a general rule, one adult may harass or bully another adult (so long as he she does not resort to actionsw which are legal in their own right, like violence, threats of violence, extortion or blackmail)  to his or her heart's content. The law does not regulate most interactions between adults, even negative ones.

The only harassment or bullying made illegal in the workplace is that directed against a person because of his/her membership in a specifically protected group or category, the main ones of which are: race, religion, age over 40, disability, and sex/gender. That is, you cannot harass a person because he is African American, or Muslim, or 55, or disabled, or because she is woman. (That does not mean, for example, that you cannot harass, say, an African American Muslim 55-year old parapelegic woman, only that you can't harass her because she is an African American Muslim 55-year-old parapelegic woman--you can harass her because she is a poor worker, or you can't stand her politics, or just don't like her as a person.)

However, apart from barring discrimination against specifically protected categories, the law does NOT bar workplace harassment or bullying--though such behavior could be against a company's own policies or rules.

To prove illegal discrimination, if you believe it is illegal discrimination, you can use your own testimony; the testimony of other witnesses; memos, emails, text messages, or other documentation, or possibly video/surveillance footage.