We cannot. Not completely and not  on our own. That is why I believe that the peer review system in psychological sciences (and other sciences) with all its shortcomings is very important and probably the best way to correct for bias. Other experts bring different perspectives on your subject matter and have a better chance to pinpoint where you're being biased in your reasoning, data analysis, etc. Other forms of peer interaction may also work as good sources of "debiasing": lab meetings, seminars, conferences as long as people are not afraid to critize (and be criticized) and as long as there is enough diversity in perspectives (to avoid biases stemming from "group thinking"). Of course good training and becoming aware of different sources of biases also helps a lot but I do not think it is enough...you need feedback from your peers.

As humans, we can't control it very much.  Even when we are aware of the biases that shape our perceptions, we are still susceptible to them.  The best way is to either create processes that reduce the impact of bias (e.g., having data analysis/interpretation conducted by someone who is blind to the research hypothesis), or to have information be interpreted by multiple people who hopefully have biases in different directions so that, in a sense, they would cancel out. Of course, the former approach is usually not feasible, and typically the people we conduct research with are likely to have the same biases we do.  But like the commenter above states, people outside of our own circles, such as peer reviewers, can serve in this function.