By default, Copernic Desktop Search is indexing when your computer is not actively in use and when the CPU is not overloaded. If other programs are running and they are using a lot of your CPU, it will not start indexing. 

Press Ctrl + Alt + Esc to open Windows Task Manager -> Tab performance -> If CPU Usage is above less or more than 50%, indexing should not start.

You can immediately update your index (depending on Indexing Performance settings) with Tools -> Update Index -> Entire Index or also try to enterely recreate your index with Tools -> Options - Advanced -> Index Location -> Click the "Clear index and reindex all" link at the bottom of the screen.

If your indexation does not start immediately, it can be because of your "Indexing & Performance" settings. To change these settings: Tools -> Indexing & Performance. Note that the unrestricted option can use a lot of computer resources. 

Verify also that your indexing is not in a Pause state:

Open menu Tools -> Disable Pause Indexing if needed.

CDS is indexing only Files specified at: Tools -> Options -> Files. Verify which folders that is indexed or not indexed and which type of file is indexed in the folder with the Modify button.

CDS is indexing only Emails specified at: Tools -> Options -> Emails & Organizer Indexing Settings. Expand your Mailbox tree and verified if your mailbox and the folders of your Mailbox you want to index is check.

CDS is indexing only type of file specified at: Tools -> Options -> Advanced Settings -> File types to index. Just click on the Add button and type the extension you want to Add.

Finally, if your scheduled indexing is enabled. Open menu Tools -> Options -> Indexing & Performance Settings -> Scheduled indexing section -> Enable "Default schedule" or "Custom schedule".