'require' keyword not being recognized by webstorm

In Webstorm, there are three places in your settings (ctrl-alt-s) where you can update settings for Node.js projects.

Settings: Javascript Libraries

First, in Javascript | Libraries you can specify that Node libraries should be loaded. Your set of libraries may look different than this, but it should be pretty close...or, if needed, you can add the libraries so that your flavor (node, io, whatever) shows up.

JSHint

Second, if you have JSHint enabled, you should also enable the Node.js environment so that JSHint acts appropriately.

Nodejs and NPM Settings

You can (should) also set the path to your node executable. Webstorm will also detect your globally installed modules, too, and show you if your versions are up-to-date.

The Official Docs

Finally, this reference link contains much more information about WebStorm and Node: JetBrains Webstorm -- Nodejs Docs

Under Preferences > Languages & Frameworks > Node.js and NPM, make sure "Node.js Core library is enabled" is enabled.