How do you know which way the current is flowing in a circuit?

In metal conductors, current is a flow of electrons. As electrons are negatively charged, they are repulsed by an external negative charge and attracted towards an external positive charge. In other Words, electrons travel from negative to positive.

Before the structure of an atom was understood, scientists such as Benjamin Franklin believed that current was a flow of some type of mysterious fluid, which flowed from an area of high pressure, to an area of low pressure. High pressure was considered to be positive, while low pressure was considered to be negative. For this reason, it was believed that current flowed from positive to negative.

To differentiate between these two theories on current flow, we call the modern theory 'electron flow' and we call the older theory 'conventional flow' (or 'Franklinian flow').

Conventional flow was established for such a long time, that a great many (in fact, probably most!) textbooks still continue to use it, even though they know the direction is the wrong way around! In my view, this is unfortunate as it can lead to confusion where there need not be any. Nevertheless, we have to live with it!

In practise, it doesn't really matter which one is used, just so long as it is used consistently. As many of the 'laws' relating to the polarity of electromagnets depend on current direction, when studying magnetism it's very important to determine whether 'electron flow' or 'conventional flow' is being used. For example, Fleming's Left-Hand Rule for conventional flow becomes Fleming's Right-Hand Rule for electron flow!