How can the antiarytmics work?

Depends: It depends on the anti-arrhythmic. Different anti-arrhythmic drugs work differently, most however aim to affect the chemical balance of the heart tissues (sodium, potassium, and calcium levels inside and outside the cells). Some, affect the conduction properties of the electrical system of the heart while affecting the chemical balance.

Different ways....: Different mechanisms. Some affect sodium channels others may affect potassium channels in the heart cells. They change different aspects of electric impulse (known as action potential) and decrease the chances of developing electrical disarray (arrhythmia). A hard concept to explain in simple terms. Perhaps someone else can do better.