What does the radiation from an antenna look like?
This image:



Is just a drawing, it has no meaning. It does not represent the radiation pattern of an antenna in any way !

Basically all antennas radiate (and receive) the EM waves in all directions. However, depending on the design it might not radiate and receive in some direction very well but it might do so in a different direction very well. Those are the red parts in the radiation patterns below.

Real Antenna radiation patterns look like this:


For an isotropic radiator in this case.

Or this one for a dish antenna:


There are as many radiation patterns as there are antenna types. 

Antenna designers generally use an EM simulator, for example CST, to calculate/simulate the antenna radiation pattern of a certain antenna structure.

How can we draw this linear polarization in the radiation pattern ?

These radiation patterns do not show the polarization. Since the polarization is usually in the direction of the length of the antenna it also depends on how you place the antenna. Of course, the radiation pattern changes with that placement also.