“Set we our squadrons on yon side”
'Squadrons' are tactical sub-divisions of an army, each a body of cavalry or infantry that could manoeuvre as a unit. Antony is ordering his forces into formation on the hillside facing Octavius Caesar's lines.
“yon side o' the hill”
'Yon' means 'that' or 'yonder' — pointing to something at a distance that is visible to the speaker. Antony is directing his men to a specific hillside position he can see from where he stands.
“In eye of Caesar's battle”
'In eye of' means 'within sight of' or 'in full view of.' 'Battle' here means an army drawn up for combat, not the fighting itself — specifically the main body or line of Octavius Caesar's (Antony's rival triumvir's) forces. Antony wants his squadrons positioned where they can observe Octavius's fleet and army and respond to what they see.
historical The Battle of Actium- TLN 1909historical topical
“the number of the ships behold, / And so proceed accordingly”
Antony is ordering a reconnaissance: count how many ships Octavius Caesar has deployed, then decide what to do. This brief scene frames the catastrophic sea battle of Actium (2 September 31 BCE) — the decisive engagement of the Roman civil war in which Antony, persuaded against his generals' advice to fight at sea rather than on land, was defeated by Octavius's admiral Agrippa.
historical The Battle of Actium