You have a couple of options to try out and see what works for your specific project depending on the recent implementation of StandardJS.
Define your own globals
in package.json:
"standard": {
  "globals": [
    "describe",
    "before",
    "after",
    "beforeEach",
    "afterEach",
    "it",
    "assert"
  ]
}
or in .eslintrc:
{
  "globals": {
    "describe": false,
    "before": false,
    "after": false,
    "beforeEach": false,
    "afterEach": false,
    "it": false,
    "assert": false
  }
}
More on ESLint's configuration.
Define an environment
in package.json:
"standard": {
  "env": {
    "mocha": true
  }
}
or in .eslintrc:
{
  "env": {
    "mocha": true
  }
}
Run StandardJS as an NPM script with the environment specified
in package.json:
{
  "scripts": {
    "lint": "standard --env mocha"
  }
}
Use a plugin
after installing the plugin (e.g. eslint-plugin-mocha)
in package.json:
"standard": {
  "plugins": [
    "mocha"
  ]
}
or in .eslintrc:
{
  "plugins": [
    "mocha"
  ]
}
Create your own, customized rules based on StandardJS
Check out this repository. The quick rundown:
Install with: 
npm install --save-dev eslint-config-standard eslint-plugin-standard eslint-plugin-promise eslint-plugin-import eslint-plugin-node
Then create a .eslintrc file by extending StandardJS and start to fill with your own rules:
{
  "extends": "standard"
}
Since StandardJS uses ESLint under the hood, you can pretty much configure it however you want it using ESLint's documentation.