Counterspell: How, what, where and when?

Casting 3rd level Counterspell

The 3rd level Counterspell spell can be cast as a reaction (even by a spell caster who already cast a spell) anytime they perceive another spell being cast (assuming they have an available reaction and Counterspell prepared.)

How to perceive a spell being cast

• If the spell has a verbal, somatic or material component, the spell can be perceived. See Spellcasting Components expanded
• It is perceived if cast using a magic item where that item has the text in its description "using your spell save DC and spell attack bonus" or where the item requires a command word to cast the spell or any spell components. This is to be consistent with Using a magical item to cast a spell
• It is perceived if cast using a scroll (See note on Magical Item: Spell Scrolls .)

Exceptions to this are the trait of Subtle Spell or any other specific feature that does the exact same thing as subtle spell. However, please note that subtle spell does not remove material components. If the spell requires material components, then it can be counterspelled (Thanks Jeremy Crawford.) Before you ask, no you can't hold your arcane focus in your pocket so nobody sees. If it requires a material component, it can be counterspelled. Note also, that a monster's innate spell casting is not necessarily subtle. Only when it requires "No components."

Who cast that spell?

Unless the spell was cast with no components (V/S or M), with subtle spell or similar type feature, or from a monster that has innate abilities and requires no components, everyone in the vicinity immediately know who cast the spell when it was cast. If the spell could not be perceived when it was cast there is no way to know for sure who cast it (in the absence of other evidence.)
Note that even if a magic item can't be Counterspelled, it's use is always obvious unless its description says otherwise.

How to know if the spell was higher than 3rd level:

If you have the ability to cast that spell (it's within your available spell list that you can prepare, in your spell book and of a level that you can cast) you immediately know the level of the spell that was used and can choose to counterspell at whatever level you are capable of.
Example: You have counterspell and are capable of 6th level spells. The evil Ducia casts a 7th level fireball at your friends. You know the spell is fireball and is higher than 6th level. You just don't know how much higher. No check is necessary for this.

If you don't meet the above criteria, then you don't know what level it is unless you succeed an arcana check. The DC for the check is 15 plus the spell's level.

If the spell is in your class but you don't have it available to you at this time you have advantage on the check. This could be a wizard spell that you simply haven't learned yet or a higher level spell that you don't have access to yet. If the spell is in your class and if your spell casting ability is not INT you can choose to do your check utilizing your spell casting ability modifier + proficiency or you can use Arcana.

No mettagaming allowed.

Once you've declared the counter spell and do the check you are committed. If you you roll an Arcana check of 20 and fail, your character doesn't know it's higher than 5th level. If you fail the check you are limited to a level 3 counterspell.
Exception: A PC can always cast counterspell at a higher level if they don't recognize the spell. If you decide that you want your character to always counterspell at a specific level (if they should ever fail an arcana check) they MUST declare that in advance of any spell casting. You can change this at any time during the game but NOT once the DM declares a spell is cast.
Example1: "The evil wizard casts feeble mind at you."

• PC: "I cast counterspell."
• DM: "At What level?"
• PC: "What level was the spell?"
• DM: "Roll Arcana check with advantage since this is in your class"
• PC: "I rolled 19"
• DM: "Fail. You've cast Counterspell at level 3. Roll to see if you succeed"

Example 2: "The evil druid casts call lightning."

• PC: "I cast counterspell."
• DM: "At What level?"
• PC: "I'd like to know what level it is."
• DM: "The spell isn't in your class, roll an Arcana check"
• PC: "I rolled 20"
• DM:"Success! It's a 5th level call lighting, Do you want to cast counterspell at 5th level?"