Atheists regularly find themselves in debates and discussions where the need for evidence is paramount. At the very least evidence is necessary when the existence of a god or gods is debated, but it's also necessary whenever the myriad of religious beliefs and claims are debated. Religious believers all insist that a wide variety of mutually exclusive and implausible claims are true. How is anyone else to determine which, if any, are indeed factual?
Well, atheists typically say that evidence is needed - others don't or, if they do try to engage potential evidence, they don't do it very well. Unfortunately, they usually don't realize this because they don't truly understand what evidence is and how it should be used. This is why it's necessary to first discuss the nature of evidence before discussing any potential evidence. That saves useless arguments later on - you don't want to argue over alleged evidence that should never have been offered for debate in the first place.
Evidence for What, Exactly?
First and foremost, you'll need to know exactly what you're looking for evidence of. Any random bit of data is potential evidence for something, but not necessarily for whatever you're discussing or debating. So you'll never be able to present appropriate evidence for some claim or critique alleged evidence for another unless you first understand exactly what the claim is and what it entails.
In fact, a major part of what any claim entails is what sort of evidence would count for or against it. So properly understanding a claim means also understanding what sorts of evidence you should be looking for (both evidence for and evidence against). Just as important is the simple fact that there's no point in having a debate at all if you aren't clear on what claim is being debated in the first place.
Arguments are not Evidence
The difference between arguments and evidence should be obvious, but some people still manage to confuse the two. An argument is a series of connected propositions designed to demonstrate the truth of a conclusion. An argument, which may make use of evidence, can be valid or invalid, sound or unsound. Evidence is a piece of data about the world which counts for or against some claim.
The confusion between arguments and evidence probably stems from the fact that some piece of data only becomes legitimate evidence if you can establish a connection between the data and the claim. This connection is made via an argument; sometimes the connection appears so obvious that no explicit argument is offered, but it's always there in some fashion. The argument, though, is not the evidence - that data is the evidence while the argument demonstrates why it qualifies as evidence (for the truth of the conclusion) and how strong the evidence is.
Anecdotes are not Evidence
To qualify as legitimate evidence that counts for or against a claim, a piece of data must be true. It must be a fact. Many people try to use anecdotes as evidence, treating stories of personal experiences from the past as if they were simple statements of fact that are true or false. It is precisely because they aren't that they cannot qualify as evidence.
Any anecdote contains multiple statements that might be true or false in varying combinations. Anecdotes are also heavily filtered by other experiences, various desires, and ideology. Anecdotes are further disqualified from being used as evidence in any sort of scientific context because they cannot be verified and cannot be replicated.
Evidence vs. Noise
There are far too many things that look like evidence but aren't and they can mask the presence of genuine evidence. This is often labeled "noise" and you have to learn how to filter it out so you can begin to recognize the legitimate evidence you need.
Much of the noise you encounter may be genuine facts, including facts related to your subject, and that makes them especially distracting. Some will appear to be facts but they're false or mistakes. Some arguments about the legitimacy of alleged evidence can actually be over whether something qualifies as evidence or is just distracting noise.