In this version change, Ionic has upgraded to Angular 4, a most recent version of TypeScript and some structural changes but starting an ionic project continues being similar to Ionic 2 so if you need more detailed information you could refer to that doc:
Ionic 2 Stack Overflow doc: Getting started with ionic2
Ionic official doc: http://ionicframework.com/getting-started
Starting up Ionic 3 project
Make sure you have the lastest version of Ionic:
npm install -g ionic@latest
After that you can start your Ionic 3 project:
ionic start
It will prompt you the name of the project and what type of Ionic Application you want to create, It also have some example projects.
If you don't want to initialize a git repo for the project, you have to use ionic start with the parameter --no-git
ionic start --no-git
To test the application you can run the following command:
ionic serve --lab
It will simulate the application in your default web browser.