You unplug the AC cord for DVR, connect an eSATA drive, plug in the power cord for the external drive, turn on the drive, plug the DVR power cord back in, and the DVR restarts using only the external drive.
There is a long thread about using eSATA drives with different dvrs. Not all drives work with all dvrs, so check the thread to find out what works with what.
Here's the ones DIRECTV recommends with the HR2x DVRs:
Western Digital 500GB (model WDG1S5000)
Seagate 500GB (model ST30500SCA109-RK)
Western Digital 1TB (model WDG1S10000)
Seagate 1TB (model ST31000SCA109-RK)
I use a Seagate 1.5 TB with NO problems, I used a 750 for several years.
Seagate seem to be reliable.
Make sure you get a ESATA cord as well, most don't come with them in the box.