The trip to Falkirk from Edinburgh is not a hard trip. Most of the trip is on the Motorway and then a small two lane road once you get into Falkirk. Then a bit of a drive (through the town) to the site of the Wheel. As only having traveled to Scotland once before I found it very easy to make this trip and it took approximately 45 minutes.
I rented from 1car1 and had no problems. Once we arrived we made our way out of the airport to the bus terminal there we spotted the bus to 1car1 and they dropped us off at the front door we rented the car and were on our way in no time.
Frequent regular trains from Edinburgh and Glasgow. Falkirk Grahamston is the town centre station (also served from Stirling).
If you take the fast train, this stops at Falkirk High, which is about a mile uphill from the centre. It is also right by the canal, and the big canal tunnel (see tip).
Some Grahamston trains also stop at Camelon, which is the nearest station to the Falkirk Wheel (15-20 minutes walk). The line from Glasgow actually passes under the canal only about 200m from the wheel.
UK train costs are ridiculous: an off-peak return from Glasgow or Edinburgh is around £6.00. And travel before 0915 or approx 1630-1830 requires a standard return, around £8.50 (Aug 05).