You do need believable evidence that cheating has occurred. If cheating is evident to you during an exam, have another instructor or TA corroborate what you have seen. If you suspect that two students have turned in the same paper, think of what you will say to them when you call them into your office. Above all, talk with fellow instructors about the problem and follow campus and department guidelines which tell instructors how to deal with instances of cheating. It is natural for academics to have strong feelings about cheating.
Some instructors experience moments of misgiving and uneasiness once they charge cheating.
These feelings are common, can occur even after the case has been decided and do not necessarily mean you have made a mistake or were unreasonable. It is extremely important to keep accurate and complete records of any data that are relevant to your class. However tempting it is to postpone or neglect this aspect of teaching, you will soon realize that careful and consistent documentation will make grading easier at the end of the semester. Maintain a separate grading book. Many departments have grade books available.