I've heard that there might be some creative ways to get to Geosynchronous Orbit that could save a lot of fuel. How might I manage to make this happen?
The lunar flyby of AsiaSat 3 is, of course, creative, but it was only necessary (and more efficient than alternatives) because of a launch failure which left it in a much higher inclination orbit than it should have. For a more typical launch, one in which a good amount of inclination is taken out by the upper stage, there is little you can do to save large amounts of fuel.
However, Boeing has been marketing an all-electric-propulsion satellite bus. While it takes much longer to reach your operational slot, the EP thrusters are much, much more efficient, and allow you to drastically decrease the mass of your bus at launch.
Once you're in GEO, there's more you can do to save fuel. Because of the asphericity of Earth and the pull of the Sun and Moon, GEO spacecraft have to perform stationkeeping maneuvers to stay in their assigned "slot", or longitude band. It's a somewhat technical problem, but there are strategies for performing this stationkeeping such that you can do it in a near-optimal way, and save a significant amount of propellant as a result. A Google Scholar search for "geostationary stationkeeping" will bring up lots of interesting papers for the technically-inclined.
The general physics behind transfer orbits is pretty mundane, you really can't save fuel using a direct approach. The key item is to thrust as close to the apogee as possible, using the highest ISP possible, and get as much thrust in as you can.
However, there is at least one very creative maneuver which has been done, and patented. Essentially, this involves raising the apogee of the spacecraft such that it will orbit the moon, and have the moon raise it's perigee, and fix the inclination. In order to do so, the spacecraft must be launched in either April or October.
This was done once to a spacecraft, which was placed in such an orbit where it was impossible to lift it to Geosync orbit, and thus was made quite useless. The satellite was originally known as AsiaSat 3, and was placed in a highly inclined orbit (51 degrees). The lifetime was reduced, and the satellite was perfectly stationary, but it was still usable, for a few years.