> Do they actually use software to place containers?
Yes. It is called bay planning software. For larger ocean-crossing ships the process is largely automated, taking into account weight, container type (normal or reefer), dimensions, rules for dangerous goods, etc. For smaller ships (typically feeder ships) the software also has to take into account at which harbor each container will get off in order to minimize the number lifts (rearranging containers to get them out). The software also has to take into account at which order the containers will arrive at the quay, which depends on on which order they are stacked in the terminal yard, which depends on which order they arrived at the terminal.
It is non-trivial logistics software, and some of the optimization problems are hard.