How do I reinstall CC without losing all my book information?

These steps assume that you can run CC. If you cannot then the only choice you have is to uninstall and reinstall the app, in which case you will lose the data and settings currently stored in CC.

First, if you are running CC V4.1.4 or earlier, upgrade to CC 4.1.5 or later.

The steps are (overview):

1. Backup CC's settings and database
2. Uninstall and reinstall CC
3. Restore the backup you made in step 1 being sure to check the box "Restore CC book database".

The steps are (details):

1. Backup CC's settings and database.
1. Start CC.
2. Go to Settings, scroll to near the bottom.
3. Tap "Backup and Restore".
4. Tap "Backup CC settings & database". Be sure that all three backup check boxes (settings, folder locations, database) are checked.
5. Enter a file name where the settings and database are to be saved. Be sure to note where this file is saved as you will need it later.
6. Press OK.
2. Uninstall CC however you do that on your device. Normally this is in Android Settings / Apps.
3. Reinstall CC using whichever app store (Google Play or Amazon) you normally use.
4. Start the newly-installed version. You will see the "No books" image.
5. asdasdasd
   Restore the settings and database you saved earlier. 
   1. Go to CC's Settings / Backup and Restore.
   2. Choose "Restore CC settings & database".
   3. Check the box "Restore CC book database". Don't uncheck the other two boxes.
   4. Choose the correct backup file (the one you made above).
   5. Press OK.

When the restore finishes CC should be showing your library. If it is showing the "no books" image, check that nothing is selected in the grouping drawer.

6. If you are running Android 5 (Lollipop) or later and if your books are on an SD card, it is likely that you will need to select the book folder again in CC.
1. Go to CC's Settings / Formats and folders.
2. Tap the "Default folder" line at the top.
3. Select "Choose Folder". The Android chooser dialog will open.
4. Navigate to the folder on the SD card containing your books.
5. Tap the "Select" line that is usually at the bottom of the screen.
6. Repeat steps 2 - 5 for each extension that has a specific folder.