Learn Icelandic: Ég fann þetta fótspor á vettvanginum. - I found this footprint at the scene.

You would use hlýt (the first-person singular of hljóta), followed by að hafa and the supine form of finna, which is fundið. The sentence becomes: Ég hlýt að hafa fundið þetta fótspor á vettvanginum.

Why is vettvanginum in the dative case here?

The preposition á takes the dative case when it indicates a static location ('at the scene'). If the action involved movement onto or towards the scene, it would take the accusative case. Since the finding happened within that specific, static location, dative is used.

Does vettvangur always mean a crime scene?

Not strictly, though it is heavily used in police and news contexts to mean 'crime scene' or 'scene of the accident' (slysavettvangur). It literally means 'field of action' or 'venue', but in an investigative context like finding a footprint, 'scene' is the most natural translation.

What gender is fótspor, and how can I tell from this sentence?

It is a neuter noun. You can easily tell because it is modified by the neuter singular accusative pronoun þetta (this). If the noun were masculine, the pronoun would be þennan, and if feminine, it would be þessa.