As seen in the panning view the UI options starts with three coloured icons which are described in the Nintendo Switch features website, although we have yet to see their individual menus.

	News: Get the latest updates on game releases, Nintendo events, announcements, and more, with your free Nintendo Account.
	eShop: You can buy digital versions of games from Nintendo eShop on your Nintendo Switch system or from the Nintendo website.
	Album: Easily take and save screenshots using the Capture Button on the left Joy‑Con. Then view, add text, and share to social networks from your album.

Next is the Controllers menu, with a console that changes control options depending on the mode and title, it needs to be intuitive and a simple L+R combination will determine the player's choice. Note that this screen comes up when undocking the console, making a quick and easy to change from pro to handheld controls.

During the treehouse stream we also saw a glimpse of this menu but with added visual feedback on the control methods supported and which controller each player is using (even differentiating the colours).

System Settings has yet to show up, but we have seen variations on the UI such as multiple accounts, dark/night theme, airplane mode and control method shown at the bottom left. Note that the image shown below seems to have a notification dot over the News icon, this should also light up the right Joy-Con Home button similar to the WiiU.

There was a glimpse of the Sleep Mode UI during Japan's experience meeting, although the definition is not that good. 

Update from the possible leak details what this menu could look like:

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Additionally the Switch loading screen was shown for Breath of the Wild,

for now it just had a black splash screen but maybe they will change that at release.

Plus the Parental Controls also have specific menus, you can watch them all here.

Source

Leak show possibilities for rows in the main menu, plus a full "app drawer"

Plus a social share glimpse via Twitter

And a sneak peek at an eShop page

Oh wow! It can even tell the colour!

Btw, does anyone know if 8player Bomberman local on 1 Switch is possible?

The back does put 1-8 players for TV or tabletop modes... although there are few asterisks there. Seems like it's possible in TV mode but tabletop needs two Switches, since the second asterisk does mention the maximum number of connections of the main unit is 4. Not sure how it is done in TV, where the first asterisk just says you need one controller per player and to prepare them beforehand.

Neat to see, I wasn't expecting this either

Oh! Thankyou for that pic! And yas! This should be awesome to play with my friends. Because we mostly have 5-6 people in our group. And it just sucks that most local games are 4 players.

Updated the OP to include the rest of the UI known so far, expanding beyond the initial detailed controller menu.

Didn't know Nintendo had already shown Sleep Mode during their experience day.
I wonder what those three tabs are at the left, maybe a multitasking bar?

No problem, I saw it come up a few hours after your post.
Just take note on the annotations, I did a quick translation with Google Translate.

You have reached the agreed-upon time limit.

I very much doubt the Child agreed to anything.

It's the overly political correctness of the british.

In America nothing is agreed-upon, just forced :D

Any info abt how the system runs? I hope its not as slow as 3ds

Runs with respect to what? I already linked a few video segments in the OP that might help.

Return from Sleep Mode: https://www.youtube.com/watch?v=rfK3jmdNVtQ&t=8m44s (~1s)
Starting BotW from Home menu: https://www.youtube.com/watch?v=qadzCB3CLlI&t=4h23m50s (~13s, to load save file ~30s)
Loading a course in MK8: https://www.youtube.com/watch?v=rfK3jmdNVtQ&t=12m10s (~10s)