Natural gas and propane are very similar gas fuels. Natural gas is less filtered than propane, which makes it easier to ship and supply. This leads to lower prices, though it requires gas lines to be installed within a neighborhood. Propane is used via residential propane tanks that can be set up in nearly any location, allowing for greater flexibility and the use of gas fuel outside of natural gas ranges.
Every appliance that uses gas has what is known as an adapter, no matter the fuel type. This adapter is the part of the gas line that is attached to your primary line from the gas pipes that your appliances (including your dryer) use. Your dryer, if you have a natural gas version, already has an adapter designed to accept natural gas. The issue at hand, then, is that it was not designed to accept the flow rate of propane.
Because adapters cannot be used for both types of gas, you need to buy a conversion kit with a new adapter and any associated gaskets and bolts. There is no single type of adapter to buy: manufacturers typically create their own conversion kits for their dryer models. GE, for example, has a conversion kit that fits all their dryers, but may not work with other brands. These adapters can cost between $50 and $70.
Before you visit a home appliance store to buy your conversion kit, make sure you have a dryer that is compatible. Not all dryers can be converted from gas to propane. Older natural gas dryers may have been designed with only natural gas in mind. Consult your dryer manual to discern whether it is convertible or not.