The only way to migrate entries are to export the Connections tables from phpMyAdmin or similar tool as a SQL file and then import the exported SQL into your new site using phpMyAdmin or similar tool. I’ve done it plenty of times, only takes a few minutes.
Oh, one last thing, if you’ve uploaded any images, you have to copy them via FTP and load them up on the new site via FTP in this folder:
Just install the plugins any add-ons and templates as you normally world.
NOTE: Make sure you do the SQL import before activating Connections for the first time. If you’ve already activated Connections, you have to drop the Connections tables before you do the import.
Hope that helps.