Axios is the recommended library for Vue for making HTTP requests. It's a very simple library, but it has some built-in features that help you in carrying out common operations. It implements a REST pattern for making requests with HTTP verbs and can also deal with concurrency (spawning multiple requests at the same time) in a function call. You can find more information at https://github.com/mzabriskie/axios.
For this recipe, you don't need any particular knowledge of Vue. We will use Axios, which itself uses JavaScript promises. If you have never heard of promises, you can have a primer at https://developers.google.com/web/fundamentals/getting-started/primers/promises.