How can I pin a specific document so I can access it easily and frequently?

Instead of pinning a file, let's switch gears: pin a command that opens the file. That's easily achieved via creating a .desktop file, which is what those icons on the dock actually are. Sufficient enough would be to have file in ~/.local/share/applications/ called importantfile.desktop and with contents maybe like so:

[Desktop Entry]
Type=Application
Terminal=false
Exec=gedit /etc/passwd
Name=Open Important Thing
Icon=/usr/share/icons/gnome/48x48/status/messagebox_critical.png

The Icon= part is optional, but as you can see you can use standard gnome icons. Remember also to use your own favorite program to open the important file - Exec=gedit /etc/passwd is just an example.

Alternative (and a very biased solution, as I am the author of that) is to use Files Indicator, which besides other things allows pinning specific files to be shown in the indicator itself and are opened by whatever default program is set for their respective filetypes.

An alternative for simpler files is to use Nautilus file manager to create a link and move it to the desktop.

For your word processing, spreadsheet and presentation documents you can navigate using Nautilus to the directory containing the file. Then right click on the the file and select Make Link a new icon appears called Link to filename. Grab this and drag it to your desktop.

Below is an animation for a word processing document called eyesome.odt and a desktop link created for it:

After the link is dragged to the desktop, simply double click on it and the application associated with it automatically opens it.

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Keyboard shortcut method Ctrl+Shift+Left-Click

A quicker method is to use Ctrl+Shift+Left-Click on the file and drag a copy to the desktop.

The subtle difference is the Desktop name is no longer "Link to filename" but simply "filename".