I had this problem too. Essentially the phone/tablet must show a popup window asking for permission to allow certificates for your computer. With your phone plugged in and adb ready, try disabling developer mode and enabling it again on the phone/tablet. After a few seconds you should see the popup that asks you to allow the PC. Make sure to check that it should remember your choice.
If this does not happen, make sure you install the driver package from your phone/tablet provider. LG has a separate download for the usb drivers while Samsung needs the Samsung Kies client. If you use Kies, download it. Get latest update. Then in Kies, in one of the menus, reinstall the USB driver. Then uninstall Kies.
Should be enough to get your PC recognized on the phone/tablet, which in turn allows you to communicate with the device.