I am thinking of purchasing a “my cloud” and wanted to know if I can automatically backup up remotely to the device over the internet from one of my laptops.
If you are talking about a single bay Mycloud then “NO” you can not. Not with the software that is standard on the Mycloud. There are hacks that can be installed but that would void your warranty. The Mycloud Mirror, I believe, can do remote backups.
You can do a forum search for “Remote Backups” and find more detail.
While remote backup from a computer is not officially supported with the single bay/single drive My Cloud units, one can use the WD Sync software to sync contents on their remote computer to the My Cloud.
http://mycloud.com/learn/?id=mycloud
https://support.wdc.com/product.aspx?ID=904#WD_downloads
