This answer varies from atheist to atheist. Some are more stringent than others.

Note, by "prove" we're using a basic definition of "demonstrate beyond a reasonable doubt".

A good place to start is a solid definition. A big struggle is that there's as many god definitions as there are theists. The definition actually has to be "provable". There's a level of unfairness in being asked what it'd take to "prove" a god that's been deliberately engineered to be un-provable. Many definitions are not falsifiable, or even testable.

After that, one would follow the scientific method. Science is the single most effective method humans have ever conceived for precisely and accurately determining what reality is, and how it works. It's incredibly picky, harsh, slow and difficult. It does a good job.

If you wish to undertake this endeavor, this might be a good process:

  1. Define what it is you're trying to demonstrate, and what its attributes are.
  2. Derive some possible tests that would demonstrate those attributes (Hypothesis testing), as well as what would falsify it.
  3. Perform those tests, gather up the evidence.
  4. Submit for good, rigorous objective peer review.
  5. If it survives the peer review, submit to the person you're attempting to convince.

Yes, it's difficult, however, we have many volumes of scientific knowledge that's managed to pass this process with flying colors, and has resulted in virtually all advanced technologies in the world today.

Often, theists will attempt to intimidate ("You burn in hell!"), or suade with emotion ("But Jesus has shown you so much love!") to convince an atheist. These typically don't work. We do have emotions like anyone else, and appreciate it, but when it comes to the matter of accurate truth about reality, it must come down to the logic and evidence.