Moving around
The first thing you need to know about using the browser is how to move around. You can scroll pages (both horizontally and vertically) by dragging them. For example put your finger on the center of the screen and swipe towards the top. The page should scroll down.
If you want to follow a link, tap it. Once clicked it should go orange and new page should load in a while.
Home page

This is home page — a page that is loaded on each start of the browser:
The big input field at the top is where you can enter URL you want to go or the search phrase you want to search.
On Screen Keyboard
Hit the big input field and you'll be presented a keyboard:

Tap the letters to enter them.
Entering the URL

Tap "Go" to start loading the page
On page interface

While the page is loading you can zoom in and out using the zoom button located at the middle bottom on the screen. On the very bottom you see what's the progress of loading the page and what's the loaded page URL.

The page's fully loaded now. Hit the home button (right bottom) to get back to the start page:
Home page interface
The pages you visit are added to the home page:

The home page displays only a few lastly visited pages, and replaces the old ones successfully with new ones. If you want one of the visited pages to be remembered and not replaced with other one, click heart icon beside it. If the heart is red, the page will be remembered as long as you don't click the heart again (and make it gray).
You can go back to any of those pages, by just tapping on them.
More on keyboard
If you want to enter special characters to URL field, tap the ⎇ key on it. It'll switch the view and display symbols only:

Tap ⎇ again to switch back to letters and numbers.
To enter uppercase letters, tap the ⇪ key:

Tap ⎇ again to switch back to lowercase.
Finally, to close the keyboard, either hit "Go" button or the red ⨯ button in the lower right corner of the keyboard.