Usually by
- checking the original publications to make sure you are repeating the experiment correctly
- checking (and monitoring) the experimental setup to make sure it is doing what you think it is doing and you aren't introducing errors
- checking the data analysis
- running "sanity check" experiments with the same setup to make sure it has no obvious flaws
- comparing with recent replication experiments by other researchers
- showing that the experiment and results are repeatable by multiple people in different organizations with their own lab setups
- consulting with the original authors (who may be helpful or unhelpful) if they are available
- comparing against other data sets
- comparing against results from analytical modeling or simulation
- looking for alternate explanations of the anomalous results and checking for whether they might be occurring
etc.
As others have noted, the same methods apply to sorting out conflicting experimental results regardless of who conducts the experiments.
But it's not easily remediable. And that is the point.
Just imagine how that would work in practice. Somebody does an original experiment that gives exciting results. Let's say they get a 1000 Science Points for that. Now somebody replicates that experiment. How many points should they get? Should you get as many points for replicating a 1000 points experiment as replicating a 500 points experiment? Why would you do original experiments at all anymore? Isn't it easier just to replicate original experiments where all of the hard work has already been done?
Awarding points for replication is a nonsense idea.
If someone replicates it after this process and finds different results, it's "new research" again and needs to be replicated again.
I think we shouldn't even accept papers that haven't been replicated twice by independent teams.
Honest researchers doing original research to the best of their abilities. That's how you get good results, and what drives progress. The rest is just bureaucracy. The need for replication will be just another bureaucratic add-on to catch dishonest researchers, and researchers who value prestige more than the truth.
I don't.