Hi, Limner!
It's simple... just spritz a paper towel with water to thoroughly dampen it. Sprinkle the seeds lightly (how thick depends on whether you're going to pick the sprouted seeds off the towels and plant them individually, or plant the paper towels as sort of a giant seed tape... you'll want to space them an inch or do apart if the latter) on the damp towel.
Lay another towel over the seeds, and spray it with water to thoroughly moisten it. If you're wanting a "seed tape" to make a wide row of carrots, you can make it several towels long.
Roll up *loosely* and stash inside an OPEN plastic bag... this helps the seeds remain moist, but allows plenty of oxygen and prevents mold growth. Place in a warm (not hot... carrots refuse to sprout at soil temps above 85 degrees) spot.
IF you are just using this to presprout seeds you will then plant individually (this can be a great way to use old seed with lower germination percentage, as you only plant the seeds that show life), check daily after 3 days or so, and transplant as soon as you see tiny rootlets starting to show. If you wait too long, they'll grow into the paper towel and will be damaged when you try to remove them.
If you're going to unroll the paper towels like a giant seed tape, you can let them go a bit longer, but be careful the roots don't start growing through more than one layer of towel.
Unroll the "seed sandwich" over a well prepared growing bed, and sprinkle a thin layer of soil over it. Keep well watered until the tiny plants get established...
Summerthyme