To expand on Love Robin's response, the method depends on how you are editing the page.
In the upper right of the editing window next to the cancel button, you should see a button that has 3 horixontal bars next to a triangle. Click this to open the drop-down menu. Click "Categories" to open the category window. Find the category you want to remove and click it to open the editing window for that category. In the upper right of that categories editing window, there should be a trashcan icon. Click that icon.
Using classic editor (both source and visual mode)
As Love Robin said, there should be some editing panes on the side of the editing window. If you don't see them, they may be collapsed. If so, look for a small triangle icon on the side of the editing window and click it to expand them. Then scroll down to the categories section and expand it if needed. Remove categories by hovering over them and clicking the trashcan icon.
Using source editor (i.e. classic editor's source mode or VisualEditor's source mode)
As Love Robin said, look for [[Category:MyCategory]] where "MyCategory" is the category you want to remove. Delete it.