Vue.js is an MIT licensed open source project and completely free to use.
However, the amount of effort needed to maintain and develop new features for the project is not sustainable without proper financial backing. You can support Vue.js development by pledging on Patreon or donating on PayPal.
If you run a business and are using Vue in a revenue-generating product, it makes business sense to sponsor Vue development: it ensures the project that your product relies on stays healthy and actively maintained. It can also help your exposure in the Vue community and makes it easier to attract Vue developers.
If you are an individual user and have enjoyed the productivity of using Vue, consider donating as a sign of appreciation - like buying me coffee once in a while :)
As of now I am exploring the possibility of working on Vue.js fulltime - if you are a business that is building core products using Vue.js, I am also open to conversations regarding custom sponsorship / consulting arrangements. Get in touch on Twitter.