There are a few ways to go about this, and it depends on your customer base. If there are going to be multiple new customers, you would want to go with the easiest approach for them. If it's going to be mostly the same regular customers, you can do the work of setting it up for them, then as they have issues in the future you can log in and take over.
Windows version of Remote Desktop Connection can have some ups and downs, but once it's set up, it's pretty straight-forward.
You would need their external IP (from something like whatismyip.com) and the port would need to be opened on their router (not something many customers are skilled at). Additionally, it's recommended not to use the default port for remote destop, so you'd go into the registry, change the port number here:
HKEY_LOCAL_MACHINE\System
\CurrentControlSet
\Control\TerminalServer\WinStations
\RDP-Tcp\PortNumber.
This would need to be done for each PC you might be servicing (then forward that new port number for the corresponding PC by its internal IP address).
The easier solution (but one that costs money) is to use a service like LogMeIn (or yes... goToMyPC). LogMeIn has free accounts, but their software has to be installed on the client PC.
I do this myself (go in and set it up) on servers that I maintain at businesses, but for people calling in who do not have the software installed (and it's a pain walking them through it--not that it's difficult, just because it could end up taking 30-60 minutes depending on how well they follow directions and how well you understand what they're seeing), it would be better if they could just go to your website, hit a link, follow some much shorter directions and give you access that way. That is the service that costs money. For LogMeIn, it's called LogMeInRescue, then there's GoToAssist.