The best way to edit an existing objective is to navigate to Objective > Overview
Click on the name of the specific Objective you want to edit to get to its detail page. From there you can edit the objective. All the fields with the Edit button can be edited, which includes:
Objective name and description
Participants (owners, stakeholders, followers)
Add/edit/delete key results
Add/edit/remove parent and/or child objectives
Note: Owners of objectives can edit all parts of an objective. Stakeholders will have limited editing abilities, while Followers will not be able to edit an objective.