How do we know whether our results indicate whether or not there is a relationship between our variables?

We can test for 'significance' in order to determine whether it's likely that the results that we see are due to random chance or due to a relationship between them. This involves using a statistical test (the details of which will be determined by the type of data that we have and how we carried out the experiment), and it will give us a value which allows us to say what the percentage chance of the results that we see having occurred due to random effects.
If that percentage is less than 5% then we can say that there is a statistically significant relationship between our variables. This should not necessarily be automatically assumed to be a cause and effect however, as there can be significant relationships between variables without them directly affecting each other, but as a by product of the effects of another variable which is not accounted for.