Learn French: Il met l'arme sur la table. - He is putting the weapon on the table.

The verb mettre (to put) is irregular. In the present tense, the singular forms are je mets, tu mets, and il/elle/on met. Since the subject here is il, we drop the 's'.

How would I say 'He put nothing on the table' to practice this lesson's grammar?

You would say Il n'a rien mis sur la table. In the passé composé, the negative word rien (nothing) is placed directly between the helping verb (a) and the past participle (mis).

If I wanted to say 'He put nobody on the table', does personne go in the same place as rien?

No! You would say Il n'a mis personne sur la table. Unlike rien, the negative pronoun personne (nobody) is placed after the past participle (mis).

Is arme masculine or feminine? I can't tell because of the l'.

Arme is feminine (une arme). Because it starts with a vowel, the word la drops its a and becomes l' to make it flow better when spoken.