You first need to install Chrome Beta for Android if you don't have it already, then open a new tab and type this in the address bar:
Then press Enter, pick "Enabled" from the drop-down below "Enable the new NTP" and tap "Relaunch Now" at the bottom of the window to restart the browser.
The updated new tab page no longer shows 3 sections. You only get a big Google logo, a search box that points you to the browser's omnibox, a list of the most visited pages and 2 buttons for bookmarks and tabs from other devices. Both buttons open new pages: the bookmarks page has a different interface (it's now a list instead of a grid), while the "other devices" page looks the same.
Chrome's blog informs that some Chrome Beta users might see the new interface automatically. "We've tested this New Tab page with a search bar on desktop and now want to bring the benefits, including a faster load time, to mobile as well. While you can search straight from the Omnibox in Chrome, we realized many users continue to visit their search engine's homepage before searching, so we wanted to make it faster for those users to search. We're always thinking about how to save milliseconds from every search you perform, and we hope this new feature will save you time on-the-go."
If the new interface has been enabled automatically, you can use the same instructions to disable it. Just pick "disabled" instead of "enabled".
The updated new tab page has some advantages: it loads quickly, it's consistent and it looks nice. Unfortunately, bookmarks and the list of tabs from other devices load in separate pages and you can no longer see them automatically when you open a new tab. I created a folder with mobile apps I frequently use and this folder used to be displayed when opening a new tab. This feature is no longer available in the new interface. Unlike the desktop Chrome, the mobile Chrome doesn't support extensions and you can't customize the new tab page.
This "baby" new tab page could be useful to help users discover the omnibox and use it to search the web, but what happens when they realize that the big search box is redundant? And what about the people who already used the omnibox?