There is a lot of potential for getting confused about polarization. Its the sort of thing you think you understand first time, skip through to the bottom line, and go away truly believing something false. Also, try and separate in your mind the difference between a far field radiation pattern (strength) plot, and the shape of the field if you took a plane slice through it, vertical, horizontal, tilted, etc.
Simply because a circle is a single special case of an ellipse, you understand elliptical polarization easily and quickly if you tackle it by first understanding
circular polarization.
..and a more or less essential step befor even that, is to understand
plane polarization.
Step 1 - have a look at the explanations and great animations on the wiki.
--->
https://en.wikipedia.org/wiki/Polarization_(waves)
Since radio waves are the same stuff as light, they behave the same, and can come polarized.
Just like light, once the wave hits a plane reflector surface, what leaves is plane polarized.
Even if you skip the heavy math, and just look at the pictures, you get the idea.
Step 2 - If you now imagine you have an antenna element, (say a horizontal one). It will make horizontally polarized plane waves. Add a vertical one with it, It will make vertical polarized plane waves. They both leave the antenna at the speed of light. They are separate, and isolated from each other. In practice, with careful construction, the isolation can be more than 30dB. It is enough to be able to use them simultaneously for separate TV channels.
Step 3 - a bit special. If you make the feed to one of them a little longer, so that it is driven delayed by a quarter wavelength, 90 degrees out of phase. Then the radiation leaving the ensemble combines as of it were were generated by a field vector rotating at the driving frequency. Here is where you need another nice animation.
--->
https://en.wikipedia.org/wiki/Circular_polarization
If you make the cable that bit shorter, so that it is the
other antenna that is driven delayed, the rotation changes direction. Here we have the two kinds RHCP and LHCP right-hand and left-hand.
Again, they are isolated from each other. You can use them simultaneously for separate signals, but the antenna assembly described above is only good for one type at a time. You could set up two antenna assemblys, one for RHCP, and the other for LHCP, knowing they can't much couple to each other.
Last step - Elliptical. If the signal strength is equal in both the vertical and horizontal components, you get circular. If they are unequal, the result is elliptical polarization.
Circular polarized signals need circular waveguides. You can gather all the energy in (say) a RHCP signal, and encourage it to come out of a single waveguide port using various tricks like a
septum polarizer.
Simultaneusly, the other channel, can use LHCP, and it comes out of the LHCP port.
Circular polarized waves arriving can be separated into their horizontal and vertical components using a
ortho-mode transducer, which does a different job. Each output will be -3dB down on the circular polarized signal strength. A pure horizontal plane wave arriving will exit with very little loss out the horiz port.
Using a ortho-mode transducer, you would notice that for a elliptical polarized signal, what comes out the ports is not equal in strength.
Finally, it is a physical fact that a RHCP circular polarized wave will change rotation into a LHCP wave as it gets reflected off a conducting surface. One has GOT to get it right, especially if using dual reflector (Cassegrain) dishes.
Hope this helps..