Squid are usually caught by means of a normal fishing line and a special hook-and-lure combination called a jig. Jigs are weighted, glow in the dark, and have several circles of upturned hooks on which the squid's arms and tentacles. Here is a squid jig (and a squid scientist) in normal use:

Here is a much more heartwarming use of the same equipment, to save baby birds from a construction site in Australia.
"It took four to five hours to get them out; physically it was too tight to get your hand in," she said. In the end, it was the gentle use of a "squid jig" (equipment used for squid fishing) that plucked the birds to safety.