You can not really figure out the gender of a noun in danish without looking it up in a dictionary. Therefore my best advice is to just learn when to use "en" and "et" by heart. Don't spend time looking it up in a dictionary, you will eventually learn them as you keep learning danish.
@NanaAnders: Yes, Danish has two genders: common (with ‘en’) and neuter (with ‘et’). In linguistics, ‘gender’ does not necessarily mean male/female; that's how gender works in French but not in Danish. (In fact, it is the influence of languages like French that makes ‘gender’ mean male/female outside of linguistics; the broader meaning in linguistics is the original meaning.)