Transfer contents of old drive to new using Disc Utility?

I just purchased a new SSD and want to transfer the entire contents of my HD in a Mac-Mini to it.

The SSD vendor advised using Disc Utility to drag & drop the old drive to the new but so far I have

been unsuccessful. I have formatted the new drive and resized the partition on the old drive to make

it smaller than the new. When I try to run the utility, it seems to initialize and begin the transfer, with

a 2 hour predicted time period to complete the process. However when I come back later nothing seems to

have been done.

Anybody have any suggestions?