Few telltale signs give away an office romance as clearly as the two suspects routinely leaving the office and returning at very close intervals. I witnessed this first-hand at a previous job, as two colleagues would disappear mid-afternoon or during lunch just moments apart and practically pull back into the parking lot at the same time. Given that one of them lived close to the office and the way they looked afterwards — the flushed faces, the messy hair — the whole office quickly grew suspicious.
The closer their desks, the more incriminating this is. Unnecessarily private conversations are a tipoff, especially if you catch looks between their screens and each other accompanied by knowing smiles or dancing eyes.
If two coworkers deny that they're friends outside of work but somehow know considerable personal details about each other, something might be up. In my former office, when the subject of tattoos arose one coworker outed another for a hidden tattoo. Busted.
Different scenario: When two coworkers I know volunteered to collaborate on a project together that normally would've been executed alone, several people around them grew suspicious. Don't assume just because a man and woman who work together seem friendly that something is happening behind the scenes — that'd be very hetero-normative of you, anyway — but if two people seem to be finding unnecessary reasons to be in each other's presence at work while claiming they aren't friends, there may be more at play.
If someone asks one of the parties involved, their response can be the most damning evidence of all. There are no dumb body language hints to look for like blinking a lot or something, but they're probably not expecting the question and might stammer through an unbelievable denial. Do not, of course, consider this permission to go on a witch-hunt in the office, but if you're close to one of the people potentially involved, sometimes it's best just to ask.