If you are using Vue cli 3, only variables that start with VUE_APP_ will be loaded.
In the root create a .env file with:
VUE_APP_ENV_VARIABLE=value
And, if it's running, you need to restart serve so that the new env vars can be loaded.
With this, you will be able to use process.env.VUE_APP_ENV_VARIABLE in your project (.js and .vue files).
According to @ali6p, with Vue Cli 3, isn't necessary to install dotenv dependency.