After you first log in you are taken to the Character Select screen where you see a listing of your characters and can pick which one you want to select. In this example I only had one character made. After you select which character you want to look at you are taken to the Gateway Home Screen.
As you can see my character was only level 9 at the time I took this picture so Professions is greyed out because you need to be level 11 to learn professions. Also I was not in a guild when I took that screen.
Here’s the Character Sheet page. I am assuming at some point the red outline of what looks vaguely like a minotaur will be replaced with an actual 3D model of what your character looks like. You can see all your stats in the bottom section and if you mouse over your items you can look at what the stats are (which helps for finding upgrades through the AH).
If you look at the left edge of this screen you will also see there is a menu which will take you to any of the other pages without having to go back to the home screen.
A unique feature of the Gateway is you can level your professions through it! The interface is really similar to what it is in game, the only downside is the duration to complete each task is longer through the gateway. You would really only want to level professions through the gateway if you are not able to login for some reason and you want to still want to level your professions.
You can also post and buy things off the AH through the gateway.
This is the view of your inventory you get when you want to put something up. Of course when you mouse over an item you get a pop-up that tells you all the detail of the item.
If you are in a guild there are a variety of things you can look at and check on from the gateway.
You can add events from the Gateway and update the information (if you have the ability to do those things in game).
What else could you possibly want to do through a web-portal? Well how about send mail to people in game!
I am not sure if once this goes live you will be able to look-up other players. You couldn’t during the beta weekend but it could have just not have been active.