Usually, if you are not a lawyer, you can represent only yourself. You cannot represent another person, and most businesses are legally "persons." Therefore, you cannot represent a corporation, partnership or other business entity. For example, the manager of an apartment building cannot represent the property owner in an eviction. That would be representing another person. If the property is owned by a business, then the business must be represented by a lawyer because the business itself is a "person." If the property is owned by a natural person, then the owner can represent herself or himself.
A parent or guardian can "appear" on behalf of a minor child or protected person, which means the parent takes the place of the child as the real party in interest, but usually a parent or guardian cannot "represent" a child or a protected person. In juvenile court, you can ask the judge for permission to represent a child or protected person. And in a petition for a child protective order any "interested" person may represent the child.
For the special rules about representing a party in a small claims case, see our webpage on Small Claims. For more information, see Rule 14-802. Authorization to practice law.