I am assuming that you have already installed Xcode.
$ /usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
$ brew install node
$ sudo gem install cocoapods
Install the forceios Package
$ sudo npm install forceios -g
Create React Native project
$ forceios create
On terminal run following command.
$ cd SalesforceReactHelloWorld $ npm start
And now go to ios (cd ios) folder, open .xcworkspace file and hit play button to run project. In my case project file is "SalesforceReactHelloWorld.xcworkspace"