When you backup an iPhone to iCloud, a PC is not involved. You go to Settings > iCloud > Backup and turn "iCloud Backup" to on. You can then tap "Back Up Now" on that same screen. Also, once it is turned on it will automatically back up when it is charging if it is connected to Wi-Fi.
If you want the backup to be on a PC instead of in iCloud, you use iTunes on the PC. The following previous discussion may help with how to use 2 separate Apple IDs with one computer: Sync two separate Apple IDs to a shared iTunes acct???
Further instructions for both iCloud and iTunes backups are at How to back up your devices using iCloud or iTunes - Apple Support
Note that backups are only usable for doing a full restore to an iOS device. You cannot view the contents of either an iCloud or an iTunes backup.