Go to a page that you would like to bookmark and click on the little star at the top right of the screen. It will pop open a little dialogue box that will let you set the bookmark, even edit the name. And yeah, absolutely nothing happens. That's because, in their infinite wisdom, they decided to not have either a menu at the top of the browser, or a place for the bookmarks to appear. I can only guess that they thought with the smaller screen, it would be a waste of space. I wish they wouldn't do that! I will gladly sacrifice 1/4" on my screen for a bookmark bar.
Now go find the three little parallel lines. I have no idea what this is suppose to represent. Possibly the number of times you will need to knock your head against a wall figuring it out. Luckily, that is the same as on the regular Chrome browser, which takes you to a bunch of stuff including settings and bookmarks. From there, you tell Chrome that you would like to see bookmarks at the top of your browser, and you can even find the bookmark manager, which is similar to the regular Chrome.
I'm sure that the designers aren't sitting around, wringing their hands and laughing manically, saying, "this will really drive 'em crazy!" I'm sure they meant well. But bookmarks are the easiest way for me to navigate on a browser, and if it is for you, too, it's worth the trouble to fight a bit to earn it.
I hope that this helps.