This ground requires you to be able to prove that your spouse had sexual intercourse during the marriage with someone other than you. You can't rely on this ground if you were the one who committed adultery. The proof has to be sufficient to convince a judge that the adultery happened. The easiest way is to obtain a written admission of that from your spouse. If your spouse won't give you that, you will have to provide other reliable evidence.
Cruelty includes both physical or mental cruelty.
An example of physical cruelty would be your spouse hitting you. Examples of mental cruelty are excessive shouting at you, or demeaning you with words, or alcoholism. Again, it will be up to you to provide sufficient evidence of cruelty to convince a judge. Because of the social embarrassment involved in these latter two grounds, and the time the court procedure can take, many people rely on the 12 month separation ground, even where there is convincing evidence of adultery or cruelty. The procedure is fairly straightforward.