If I press ctrl+A the font selection is greyed out. So how do I make sure I’m using Times New Roman in all parts of my large document?
As you did not mention OS, LibO version and where the Font selection is grayed out, I cannot give you a specific answer but made a test in LibO 4.2.4.2 running on XP.
If I do ctrl+a the entire text is selected.
1 - Right click allows me to choose the “Font” item and than select a font.
or
2 - Right click and select “Characters” and choose the font you need.
or
3 - Format > Characters and choose the font you need.
When working with “Character” settings, make sure you only choose the font. Otherwise you overwrite all other features like bold, italics, smaller or larger characters etc.
As you mentioned you have a larger file, I recommend you to read about Paragraph Styles in the free manual. This is an excellent feature of LibO Writer. You can use F11 to open the Style window. The free manual you can download from: http://www.libreoffice.org/get-help/documentation/