One of the first questions that must be solved when designing an aircraft for Titan is the propulsion system. Obviously, a simple chemical rocket could be used. One attractive propellant combination would be a methane/LOX engine. Water ice is believed to exist in quantity below the surface of Titan, and from this LOX can be made. Though the majority of the atmosphere of Titan is nitrogen, methane is also present, and the quantity increases at lower altitudes (up to about 4-5%). The surface hydrocarbon deposits also contain massive amounts of methane, as well as other hydrocarbons such as ethane and propane, which could be used as fuel or refined into methane.
However, chemical rockets are inefficient, so what other options are there? One exotic option, suitable for a large aircraft, would be a nuclear turbine, similar to the J87. Operation would be very similar to on Earth: the incoming Titanian atmosphere would be heated by the nuclear reactor, then expelled at high speed, producing thrust. This concept would have the advantage of virtually infinite range (though this would be of somewhat less consequence on a small body such as Titan). However, the mass of the reactor and shielding would severely cut into payload, making this method only suitable for a very large aircraft.
Aircraft on Earth carry their fuel with them, and harvest oxidizer from the atmosphere. What if we reversed this? What if our hypothetical Titanian aircraft instead harvested fuel from the environment, while carrying its own oxidizer?
We will use liquid oxygen (LOX) as our oxidizer, and methane as our fuel. The atmosphere of Titan has a pressure of about 146 kPa at the surface, and about 4% of this is methane. This means that the partial pressure of methane at the surface is roughly 5-6 kPa. This is close to the partial pressure of oxygen in Earth's atmosphere at an altitude of 10,000m. Given that operation of conventional jet engines is possible and that altitude is possible on Earth, it is reasonable to assume that there will be enough methane for our engine to operate on Titan, at least at low altitudes.
Analysis of the properties of methane indicates that it will be liquid at Titan's surface. On the other hand, nitrogen exists as a gas in Titan's atmosphere. This is useful; through careful design of the inlet, it would be possible to separate the methane fuel from the useless nitrogen. With the methane obtained, and liquid oxygen carried on board, our engine would function similar to a liquid air cycle engine. (More info on this type of engine can be found here). Though the specific impulse of the engine itself would be approximately the same as a conventional methane/liquid oxygen engine, the elimination of the need to carry fuel would dramatically increase payload and efficiency.
Alternatively, rather than separating methane out from the nitrogen, the Titanian atmosphere could be inducted in a gaseous state. This would allow a Brayton cycle engine to be used, as is done in a conventional jet turbine (LOX would again be used as the oxidizer). Though I have not yet done the math, it seems to me as though this would offer increased efficiency over the previous option (the Liquid Methane Cycle Engine?), though less thrust. Which option is better for our far-future Titanian aircraft would depend on the specific application.