If the drive is higher than the surrounding ground, and it's not rocky where you want to run it, take a 1 1/2" PVC pipe, start digging a hole beneath the driveway and use a hose to wash out the dirt in front of the pipe. Stop every once in a while to pound the pipe further under the drive, and wash out more dirt. The dirt usually comes back out of the pipe with the water. Keep doing that until the pipe comes out the other side. The same process can be done with a trench/pit on one side and a pit on the other. If your aim is good, the pipe will end up in the pit on the opposite side of the driveway.

For the remainder of the trench, I've rented walk-behind trenchers - much easier and quicker than hand diging a trench.

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3/4 to 1 1/4 ac pond LMB, SMB, PS, BG, RES, CC, YP, Bardello BG, (RBT & Blue Tilapia - seasonal).