Here are some common places where you might find a downloaded PDF file:

Default Downloads Folder:

Windows: Probably at "This PC" -> "Documents" -> "Downloads".

macOS: Inside the "Downloads" folder inside your user directory.

Linux: Often, in a "Downloads" folder inside your home directory. Locations may vary depending on the distribution. Application Specific Folder:

If you opened the PDF in a specific application (such as Adobe Acrobat Reader, Preview, or a browser) before you downloaded it, then the file may be saved in that specific application's specific folder. You simply have to check the options of that application or its recent files list.

Cloud Storage:

If cloud storage is enabled, then the PDF file might have been automatically synchronized with services like Google Drive, Dropbox, or OneDrive.

Your Device's Search Function:

Look for the PDF using your computer's search application, whether that is Spotlight on a Mac, Windows Search, etc.

If you still cannot locate it:

Check in your browser's download history. Most browsers show you all the files you've downloaded recently in such a section

Try searching within your browser's preferences. Some browsers allow you to change the default download directory.

Use third-party file search utility: There are countless free applications which will search your whole computer for any particular file.

Once you locate the PDF you may open it by:

Adding the double-click action: It should usually open PDF in your default PDF viewer.

Adding the right-click action followed by 'Open with': This will allow you to select a specific application to open your PDF.

Need further assistance?

If you want to provide more details about from where you downloaded the PDF or what you're using, or even what you've tried so far, that's where I'd be able to help out more.