I know my grandmothers complete name, date of birth, and I have tried to look for her parents to add
Julia Szent-Györgyi ✭✭✭✭✭
Step 1: find out what records were created about the event or people you're researching, and find out what has happened with those records since they were created. Are they considered public record, or are they still private? Were they ever copied/filmed/digitized? Who has copies/films/images? Are they online? Have they been indexed (made computer-searchable)?
Further steps depend on the answers to step 1. The FamilySearch Wiki can be a good starting place for finding some of those answers.
Keep in mind that vast as it is, not everything is on FamilySearch. The date, place, and type of an event (such as your grandmother's birth) will determine whether there is a record in the first place, and if there is, whether it is public or not; even if it is public information, it may not have been made publicly accessible (yet), and even if it has been made accessible, that may be at the county archives or something, not online. (And continuing the thought process, even if material is online, it may not be on FamilySearch, and even if it is on FamilySearch, it may not be indexed.)0
Do you know where she is from? I have found that you need to check for different variations of the last name and even first name. Many folks didn't know how to read nor write, so they had to hope that the priest wrote their information correctly. I have found 10 different variations of my mother's last name.0