The second law is the loop rule's twin, and it is conservation of CHARGE. Charge is neither created nor destroyed at a wire junction, and a junction has nowhere to store any: whatever arrives in a second must leave in the same second. That is the whole argument.

$I_{in} = I_1 + I_2 + I_3$ — read aloud I-in equals I-one plus I-two plus I-three. $I_{in}$ is the current arriving at the node, in amperes; $I_1$, $I_2$ and $I_3$ are the currents leaving by each branch, also in amperes, and the subscripts are just labels for the branches in the order the drawing lists them. A node, by the way, is any point where three or more conductors meet — and electrically it is one point, however much copper it is spread over.

The sign trap is the one worth rehearsing, because it is not really a trap: it is the method working. You are allowed to ASSUME a direction for an unknown branch current before you know it, and you should — pick one, mark the arrow, and stay faithful to it through every line of algebra. If the answer comes out negative, the current is real and the arrow was backwards. Nothing has gone wrong. Redraw the arrow and carry on; the magnitude was right all along.

The site version of this law: the feeder conductor into a distribution block is always the fattest thing in the box, because it carries the sum of everything the block feeds. If it did not, the node would have to store charge, and copper does not do that.