secure remote access help

Whistlestop

Need some help. Done searches on google for this type of stuff but am unable to come up with a solution. I want to be able to remotely access (not remotely control) my home PCs from the company I work for as well as other places which may or not have secure networks. So basically I'm using another PC which doesn't belong to me and I want to be able to securely access my network anywhere, browsing the files like I would do via explorer or similar.

I remember hearing from a work colleague some time ago before he moved on how he had setup a VPN tunnel between his home router and his Samsung galaxy phone. As a result while at work he'd use work's internet connection(wireless) on his phone and then be able to "VPN into his home router" and access/browse his files using the likes of ESfile explorer. Apparently this made it secure. I assume the same thing could be done if he was in say for example a shop offering free wireless access for customers?

His router supported DDWRT. Mine does not but it does have options for VPN.

Can what I'm suggesting be done?