Can't make a comment on the original question yet - but this isn't a duplicate of the other question mentioned in the comments - that one focuses strictly on how a religious text/book might be able to prove that a god wrote it. This is much more general to any evidence
Evidence for God or god(s), other than purely philosophical constructs, comes primarily in the form of legal/historical proofs. While there is science involved in aspects of proving the historical nature of religious artifacts, writings, etc., primarily it is based on testimony and circumstantial evidence cases.
First class - historical proof of religious artifacts / writings / people. For example, was Jesus a real person, and what facts from the Bible can be reasonably concluded to be historically accurate from the account. Same question for the writings and people involved in the founding of any religion. Was Mohammed real? What is the likelihood we have the original Quran or Bible intact, does the historical evidence (archeology, etc.) support the text, or is there doubt in it's historicity? How much is myth, how much is real?
Second class - historical eyewitness testimony. Mostly related to historical documents (i.e. if we believe, for example, that the Gospel of Luke is more or less historically accurate - whatever we believe of the miracles therein, then it is an account of a man who had direct eyewitnesses as sources). The question here really goes to the veracity of the witnesses, and what you believe about whether they are telling the truth or not, and if the recorded accounts are accurate in part or whole. What were their motives, etc. Similar to whether a juror believes a witness in court or not (whether they were intentionally lying, misleading, omitting, telling the truth, etc.). Any case where there is a report, but the people involved cannot be cross examined.
Third class - personal accounts from people we have direct access to, today. If someone experienced a healing, for example, can we talk to them, access their story? Can we follow their healer around and document new cases? This also relates to people that have a religious experience of any kind. If I know of people who have "become saved" and have changed their life, and I talk to them about it, their testimony is evidence to me - not just what they say, but also how their actions/life has changed can be evidence
Fourth class - personal experiences of the supernatural or "presence of God". This class will not be a large evidence to other people (though it might have minor impact - see Third Class above), it will, however, have the largest impact on you, the one experiencing it. This could also be true of witnessing a miracle, but not being the direct actor or receiver of it.
Basically, historical/legal arguments require that a case be built up, and each person will have to determine separately what their level of proof is.
For more information on the general theory (i.e. legal/historical proof of religion), plus a large amount of historical / legal evidence specifically related to Christianity / the Bible, see "Evidence that Demands a Verdict" by Josh McDowell.