Cool

Awesome spell. A really cool addition to the Spirit Guardian Barbarian, as well! I love the idea of a barbarian known for his savage oppression calming down and meditating with his spiritual mentors to foresee things. 

I just wish divination wizards could use it

Ask your DM, as a DM myself I let my diviniation wizard use it.

The description for the wizard implies that they can cast this spell

"Crouching on the floor in a dungeon intersection, a gnome tosses a handful of small bones inscribed with mystic symbols, muttering a few words of power over them. Closing his eyes to see the visions more clearly, he nods slowly, then opens his eyes and points down the passage to his left."

This is clearly describing the Augury spell, so why can't Wizards cast this if its literally in their description?

The thing is that this spell calls upon a higher power and the wizard does not draw power from a higher power like a cleric. 

Anyone got good examples of divining items they use?

I use the eyes of my Master. I take my Master's mummified head with me. Through his eyes I can foresee all type of things.

Quote from rubywolf64 >>

Cool

Quote from Mussij >>

Anyone got good examples of divining items they use?

By throwing bones one can read them by their placement and position. Use that and you can apply it to other items like feathers, leaves, sand, blood spatters, etc.

Molybdomancy is a technique of divination using molten metal. Typically, molten lead is dropped into water and the resulting shape is read to predict your future. Astromancy (or astrology) looks to the stars for answers. But my fave is the Haruspex who reads the entrails of animals (or enemies) to deduce the will of the Gods. 

Some sources say that this spell can optionally be learned by wizards. Anybody knows if it can be added using Ritual Caster feat?

Should this be tagged as Wizard now that Tasha's gives this as an Additional Wizard Spell?

Great discussion here: https://www.reddit.com/r/DnD/comments/b9wtq3/the_spell_augury_an_interesting_one_wondering_if/

Examples for Augury:

• The cleric asks "should I open this door without taking any countermeasures against traps." The door is trapped, so the spell returns "Woe."
• The cleric asks "should I venture into the room hidden beneath the statue?" That room is filled with treasure and nothing dangerous, so the answer is "Weal."
• The cleric asks "should I fight the dragon to try and win his gold?" The dragon is a dangerous enemy, but one that the cleric and the party can probably defeat without losing anyone, and if they do they'll have the opportunity to seize her treasure. That course of action has significant but not overwhelming risk, and a big potential payout, so the answer is "Weal and Woe."
  
  

Druids gain access to this spell for their Druid spell list, from Optional Class Features in Tasha's. pg. 35

Does the otherworldly entity always tell the truth? Do you know what otherworldly entity is answering?

You would think it would. 

It was originally a cleric spell, so yes it's reasonable to say you know what entity/force you are consulting and it will be honest with you, unless you invoke the repeated use caveat in the description. This divination is meant to be more narrow than tricky. Anything else interfering with or altering the response would be a DM call and probably not something to be done without consulting the players at the start of the campaign.

Quote from Dartagnan_Galochio >>

Should this be tagged as Wizard now that Tasha's gives this as an Additional Wizard Spell?

 I agree. If you have purchased Tasha's you get access to the new spells listed but the programmers have failed to make this spell and enhance ability, speak with dead and divination available. Surely this is an oversight.(Well done programmers you can now add these to your wizard.

Tasha's Cauldron says they can

Could be used to tell if the top card of a deck of many things is bad or not.