Hey Adrienne. I could see how your family's information not matching what your finding would be confusing.
What you want to start with is what you're sure of, or nearly sure of. Parents' names, grandparents' names, parents birth dates, grandparents' birth dates. In general people don't lie about these who are your direct relatives unless they're uncomfortable about their age or something. Your grandparents, if alive, may know the names of their grandparents, and will definitely know the name of their own parents.
From there, you have a whole bunch of information you can actually research to confirm. If you lack an Ancestry account, you won't be able to confirm as much, but you can use FamilySearch (it's free... might require an account now) to look up records to verify what you were told. It is safe at this point to rely wholly on research.
If you have any ancestors (parents, grandparents, great grandparents, etc) who were adopted you're going to have to either be in a state or country with lax adoption laws or you're going to have to get your DNA tested. For example, if you are looking for your father's family and have a brother who shares the same parents as you - a full sibling - you can have your autosomal DNA tested and your brother's y-DNA tested. y-DNA follows the male line (father to son only). If your mother is alive, you can also have her autosomal DNA tested so that you can compare your matches to hers - if they match you but not her, they're from your father's side, and you can use this to figure out who you're related to how.
In short, it's a lot of detective work and may cost you a fair amount, but very doable.