gnuplot has a very good help/documentation build in. Just type help plot or help vector to learn more on how to plot vectors in gnuplot.
The 2D vectors style draws a vector from (x,y) to (x+xdelta,y+ydelta).
A small arrowhead is drawn at the end of each vector.
4 columns: x y xdelta ydelta
This means, your input file should have 4 columns, where the first two columns define the starting (x,y)-position of the vector/arrow and the last two its (x,y) direction:
# file.dat
0 0 .5 .5
0 1 -.5 .5
1 1 1 0
Now typing the following command
plot "file.dat" using 1:2:3:4 with vectors filled head lw 3
gives the following output:

Drawing vectors with the set arrow command
Consider using the set arrow command, if you only need to draw a few vectors/arrows (e.g. to highlight some points in the plot).
set arrow 1 from pi/2,1 to pi/2,0
set arrow 2 from pi*3/2,-1 to pi*3/2,0
plot[0:2*pi] sin(x)
