I will say you my experiences so you can imagine how it is in Europe, in my home and neighbouring countries.
Usually, I rent airplane from same operator. The operator has agreement with several airports regarding landing and handling fees, fuel etc. It means that when I land at airport, I do not pay anything. Parking, landing and handling fee is charged from operator. I pay to operator full price that includes airplane rent, fuel, parkings, landing fee.
But now, some things have been changed, so I pay less price to operator, but I am responsible to pay fees at the airport when I land. It means I have to have cash or credit card with me. I get invoice for that.
Usually, parking is free for the first 4 hours. After 4 hours, I pay 2 EUR per ton for 24 hours parking. It means that with C150 with MTOW 730 kg, I pay 2 EUR per day for parking. For C172 which is a little bit over 1000 kg, I pay 4 EUR per day.
For small grass strips, I contact operator and sometime they have parking fee, sometimes not.
Hope it helped,
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