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During today's session, the Bad Guy used Scrying to spy on the party (as the Bad Guy has met the party before), and then used a Teleport spell to send some monsters to attack them. I wasn't sure how to describe the monsters appearing; the spell just says the targets "appear where you want to". Is there a flash of light, or a sound, or anything? Or just suddenly and silently they're just there?

The main reason I want to know is to figure out whether there's some indication that the party's Wizard could use to help determine that the reason the monsters appeared was a Teleport spell, as opposed to some other form of magic (or something that was just inherently part of how those monsters behaved).

I could certainly just make up an answer, or allow some sort of Arcana check for identifying what the cause was, I just wanted to know if there was any precedent (perhaps from other editions) that I should be aware of before just making something up.

There is no set visual or audible cue defined in the spell, so it is left up to the player and DM to figure out what spell effects look like.

However, there is a way to identify magical effects: the Arcana skill.

Arcana. Your Intelligence (Arcana) check measures
your ability to recall lore about spells, magic items,
eldritch symbols, magical traditions, the planes of
existence, and the inhabitants of those planes.

The creatures being teleported could visually give away the spell through teleportation mishaps.

It seems you really want to find a way for your wizard to figure out that it's a teleport spell. One way you could give away the fact that teleport was used would be to have a mishap happen to one or more of the monsters. Since the BBEG is scrying them, his familiarity of the area could be casual or surface level, making the likelihood of mishaps skyrocket.

Mishap. The spell's unpredictable magic results in a difficult journey. Each teleporting creature (or the target object) takes 3d10 force damage, and the DM rerolls on the table to see where you wind up. (from PHB, pgs. 281-282)

It could be that 2 of your monsters come through fine, but the third one appears 10 seconds later beat up and bruised from the mishaps. This would be a visual indication that something is amiss. You could then ask your wizard to make some sort of Intelligence (Arcana) check to learn the nature of these events. These would be reasonable grounds for asking a player to give a skill check. Alternatively, you could just tell the wizard that he would recognize it to be the effects of a teleportation spell.