You will need to make sure that the software supports the Export function. To do this, access the File > Export and choose a format that you can import later, then uninstall the application and use the setup package (in case there is one) to migrate it to another computer. Use a USB flash driver to transfer the backed up data and then use the same File menu only to choose Import instead of Export. Load the data (might take a while if it's a big file or if there are many files) and that's it. Save the whole content on the new computer from the Save menu and you will have a working application and the data migrated.
