This guide attempts to ease communication in small squads with a loose command structure, with a focus on reducing the number of friendly casualties, whether from team kills, or from unidentified enemy fire.
90% of communication is attempting to describe your position, or that of a threat. The examples will use an imaginary attack on the Stronghold on Customs.
Location callouts should never require the intended recipient to be aware of what you're seeing. "Left side of a sandbag" is an okay callout for someone standing next to you, but a friendly might be flanking. It's better to say "On the left side of a sandbag, looking from skeleton".
When calling out a position, whether yours or that of a threat, do not start from the most precise callout ("Left side of a sandbag"). Chances are, the precise callout has similar locations that can be mixed up by the friendlies, especially when the squad is operating across the entire map.
Start coarse, then refine in steps: "1) Stronghold, 2) skeleton side, 3) left side sandbag". Imagine if it was your job to hone in an artillery strike on an enemy position. Each location follow up should further narrow down the target.

As you walk around, start mapping areas you’re observing and are likely to spot a threat at. If a threat appeared in front of you, what would you tell to your teammates? In what ways would that call be ambiguous? What could you do to clear it up? If you keep repeating this loop in your head, you’ll have a clear callout prepared for when you spot someone. This especially helps if you struggle to do quick callouts. It’s both mental callout practice, and it’ll eliminate any tip-of-your-tongue stutter.
Callouts like "I see him, I see him" are unnecessary. Where? Who are you seeing? Confirmation of visual contact is relevant, but you're polluting the communications if you don't immediately switch to detailing the target location.
If a teammate is anchoring an angle, visualize the area they're protecting. If you're about to enter the killzone, announce your presence before entering.

A: "I'm watching main stairs towards warehouse 4." B: "Roger."

→ 5 minutes later B is approaching A's killzone cone.
B: "I'm pushing into your killzone A."
A: "Copy that, come on in."