Squid don’t just make sperm: they package it up into fairly elaborate little torpedoes called spermatophores, which are either handed to the female with a specially modified arm called the hectocotyl arm, or squirted onto her with a penis. Once on the female (or a male, it really doesn’t matter), the spermatophore everts, forming a structure called the spermatangia, in which all the packed sperm uncoil, ready to do their job, and the whole mass is anchored to the target with a cement body. These structures do show species-specific differences, but here is one example from Heteroteuthis dispar.

Heteroteuthis dispar. Spermatophore (a) and spermatangium (b)
Now the curious observation: squid are often captured festooned with spermatophores and spermatangia, and in many cases, the spermatangia may be imbedded deeply into the musculature of the animal — so it’s not simply as if the spermatophores are lovingly placed in an appropriate orifice, they are piercing the female (or the male, again, they don’t care that much), tearing deep into the interior. The question is, how do they get in there?
A few simple observations have revealed the answer. Spermatophores can be triggered by a gentle squeeze, at which time all of their fertilization machinery will fire. Here are some photos of some spermatophores going to work on a squid carcass.

mm) and initiation of the spermatophoric reaction by pressing on the ejaculatory apparatus with a forceps. (B)
Same specimen, but submerged in seawater, showing the ejaculating spermatophores. (C) Exterior view of
implanted spermatangia in tissue of a female, showing the site of penetration and part of the amber ejaculatory
apparatus. (D) Interior view of same spermatangia, showing the sperm mass and the amber ejaculatory apparatus.
(Read the caption carefully. That’s a human triggering sperm to ejaculate into a dead male squid. It’s gay necrophiliac bestiality! You don’t see that in the papers every day.)
The answer is that spermatophores also release digestive enzymes and actively burrow into the target tissue. Squid sperm show an aggressive persistence and vigorously active assault on the female body that our own pathetic human emissions lack…I feel a little inadequate, but I’m sure women are a bit relieved.
Another interesting observation is the function of the squid penis. It seems to be less an intromittent organ than a kind of hose to direct the ejaculations onto the female. In natural situations, unlike the photographs above, it is responsible for initiating the spermatophore reaction. Each spermatophore has a threadlike extension of a surrounding membrane, and tugging on that triggers the reaction. It’s like a squad of paratroopers leaping out of a phallic airplane, each attached by a static line that yanks the rip cord as they emerge.
Hoving HJT, Laptikhovsky V (2007) Getting under the skin: autonomous implantation of squid spermatophores. Biological Bulletin 212: 177-179.