Teamviewer is free, for personal use, remote control software and allows you to connect to a remote computer from home. Both computers need Teamviewer installed and set up.
There are different connection options - always connected, connected when windows boots or initiated by client. I use Teamviewer to help fix minor issues for friends and family.
LogMeIn, was free, but is now a paid for only option, I found it slightly easier to use than Teamviewer and each remote computer was listed, making it easier to connect to a specific computer.
I think your main issue will be persuading your clients to allow remote control software to be installed on their computers, think carefully how you present this option.
Hope this helps.