The transactional leader works through creating clear structures whereby it is clear what is required of their subordinates, and the rewards that they get for following orders. Punishments are not always mentioned, but they are also well-understood and formal systems of discipline are usually in place.
The early stage of Transactional Leadership is in negotiating the contract whereby the subordinate is given a salary and other benefits, and the company (and by implication the subordinate's manager) gets authority over the subordinate.
When the Transactional Leader allocates work to a subordinate, they are considered to be fully responsible for it, whether or not they have the resources or capability to carry it out. When things go wrong, then the subordinate is considered to be personally at fault, and is punished for their failure (just as they are rewarded for succeeding).
The transactional leader often uses management by exception, working on the principle that if something is operating to defined (and hence expected) performance then it does not need attention. Exceptions to expectation require praise and reward for exceeding expectation, whilst some kind of corrective action is applied for performance below expectation.
Whereas Transformational Leadership has more of a 'selling' style, Transactional Leadership, once the contract is in place, takes a 'telling' style.