Ground/earth loops are caused by a system being grounded at more than one point, forming a loop that acts as an antenna for noise. Breaking one of the ground connections is the way to cure them (which is why a lot of pro audio gear has "ground lift" switches). On a pedalboard the loop is between the audio ground and the power ground, so you break one of them - and usually the audio ground is the easiest.
So take a patch cable and clip the earth off one side of the cable, in the plug. The ground between pedals is still connected via the daisy chain, so audio still flows, but the loop is gone. Usually you can find the one unit causing the loop and just use lifted patch cables on either side.
Some graphics I made a while ago:
Two pedals with separate power supplies. Audio and power ground are connected, but there is no loop.
With a single supply a loop is formed between the ground points.