If you have recently received a new device and it is on the same platform as the previous device (Eg. iPhone to iPhone), you will want to complete these steps.  If you have switched platforms (Eg. Android to iPhone) see links at bottom.

Apple iOS devices (iPhone, iPad, iPod Touch):

1. Go to the same PC/server where the Act! database resides.
2. Open the Handheld Contact desktop application.  
3. Click on Maintenance; choose Resend All Data to Handheld. 
4. Select your account and press Send All.
5. On the device, open the Apple App Store.
6. Do a search for “Handheld Contact”.  Download Handheld Contact Classic.
7. Run the Handheld Contact application.  Enter the username (email address) and password.  Press Login.
8. Wait for the PC to finish syncing from Step 4 and then press Sync Now on the device.
9. Delete Handheld Contact from old device (if possible).

Android smartphones and tablets:

1. Go to the same PC/server where the Act! database resides.
2. Open the Handheld Contact desktop application. 
3. Click on Maintenance; choose Resend All Data to Handheld. 
4. Select your account and press Send All.
5. From the Android device's native internet browser visit: http://www.handheldcontact.com/ota.
6. If entered correctly, this will take you to the Google Play application.  It will take you directly to the Handheld Contact Classic download screen.
7. If the OTA link from Step 5 does not work, go directly to the Google Play Store on the device and search 'Handheld Contact Classic'.
8. Click on "Install" and download the application.
9. Once the Download is complete, you can press the "Open" button or launch Handheld Contact from Application list.
10. Enter you Handheld Contact account username (email address) and password.
11. Press "Sign in".
12. If you have already set up and resent all data from the Handheld Contact computer application, then choose "Sync now".
13. Once the sync is finished, you should be all set to go.
14. Delete Handheld Contact from old device (if possible).

Also see: http://support.handheldcontact.com/Knowledgebase/Article/View/113/0/installing-handheld-contact-on-a-new-mobile-device-if-you-are-an-existing-subscriber

NOTE: If you have switched platforms and moved to a new device (Eg. iPhone to Android), you will need to see:

iPhone to Android

Android to iPhone