The next section prohibits using oaths to establish your truthfulness.
The church has generally interpreted this as pertaining to casual conversation, in which disciples are not to invoke God or something else holy to establish the reliability of their word, but the teaching is that it does not include formal situations in which an individual's word may not be good enough because his or her reputation is not known. “Let your yes be yes and your no, no” (Matthew 5:37) means that if you become known as a reliable and truthful person, you will not need to swear to everything. This is likely an extension, by Jesus, of the Old Testament's strict application of “you shall not take the name of the Lord your God in vain.” The extension is, don't use any name in vain.
The generally accepted interpretation of the next paragraph, teaching his disciples not to use force to oppose evildoers, has been that it applies to individuals in one-to-one situations but not to civil authorities, who have social obligations to keep order (for example, a police officer cannot forgive a lawbreaker on the basis of his personal ethics, but must act on behalf of the government or the whole society). In other words, don't be a bully, and turn the other cheek rather than use violence, but keep civil order. St. Paul has more to say about this later in the New Testament.