These new feature has been automatically available when you login to gmail, Just use it by clicking Ok,got it button,Also you can switch to old inbox UI anytime by changing settings,
You can simply drag and drop the mails to desired tabs, if you got the promotional mail, affiliated mails from your friends or by spam, just drag and drop it to Promotion tabs, Gmail automatically understands and keep them and maintains for further mails, Also same for social networks notifications, feeds, etc.
You can create, edit ,hide the tabs in new interface, Gmail automatically labeled three common tabs like Primary, Social, Promotions. you can also add new tabs according to thier usage like updates, subscription, company mails, personal mails , etc. the starred mails have been shown under the Primary tab,
for more help, You can visit Google support page Inbox tabs and category labels
Problem persists comment below,