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If you see the anatomy of a LNA sitting at the top of the dish antenna, you will notice two short wire segments (perpendicular to each other) that act as antenna. Now you have the following possibilities:
1. None of them get any voltage- there is no signal;
2. The horizontal one gets signal but the vertical one does not: the signal is having horizontal polarization;
3. The vertical wire sees some signal but the horizontal one does not: the received signal is vertically polarized;
4. Both the wires get to see some signal: the signal is circularly polarized.
It is still possible to differentiate the LCP and RCP signals but that is another story altogether.
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