A vector is an arrow with both "magnitude" and "direction." To add two vectors, simply add their components (x, y); visually, the diagonal of the parallelogram formed by the two arrows is their sum. Drag the endpoints of the blue arrow (A) and red arrow (B).
Parallelogram method: Draw A and B from the origin. From the end of A, draw a line parallel to B; from the end of B, draw a line parallel to A. Their intersection is the point reached by the green arrow from the origin; that arrow represents A+B. (You can also learn addition using the triangle rule, where one arrow is placed after the other. Both methods give the same result — for a deeper look at the triangle rule and the dot product of vectors, see the Vector Lab.)
Vector A (drag to adjust) Vector B (drag to adjust) Sum A+B