The only way that I know of - also known as the freemium concept - to convert a large userbase of free users to a paying userbase is to provide a lot of new features under a premium banner that you only get access to when you pay.

Over time the weight of the new features starts to be larger than the 'simple' free version. The free version is the hook that you use to get people to use the service and to stave off encroachment by competitors.

If a free competitor should arrive on the scene that offers part of your premium features for free then you can choose to selectively offer those features to all your users (not just your paid users) but here you have to be careful not to erode your paying userbase because it is possible that people are paying for just that one feature and they'll possibly cancel their subscription.

This is not as trivial as it sounds.

For the record, I manage a website that has an active userbase of about 100K people a small percentage of those are paying users.