When I attack an enemy so far I've only been able to send one unit at a time, which doesn't always work- how do I make multiple units move on the same objective at once?
You can create armies by getting a great military leader. Every time an Elite unit (5 hitpoints) wins a battle, you have a chance of getting one.
A military leader can form an army and you can put up to 3 (or 4 with the Pentagon wonder) units into it, who will fight in unison. Armies are exceptionally powerful tools.
Later in the game, after getting the military tradition tech you can build a military academy, which allows the city to build armies without a leader.
Apart from that, there are no ways for units to fight together, this is how the game mechanics work in every civ game. In fact, you only have armies in Civ 3 and Corps/Armies in Civ 6 as your only ever options of using multiple units at once.