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In Harry Potter we are introduced to Kwikspell course in The Chamber of Secrets (and never hear about it again).

We see Filch taking courses, presumably by mail.

The descriptions of Kwikspell make me think it is for people who are weak in magic (kind of like how Neville was supposed to be when he was younger), but had magic in them nonetheless.

However, Ron's comments later in the chapter make it sound like it is mainly for Squibs to learn magic.

However, it is strongly implied through out all the books that Squibs are essentially Muggles, and will never be able to do magic.

How then is a Kwikspell course supposed to work? Do we have any information to know if it works at all? Is it a scam?

An answer from any level of canon is welcome.

Kwikspell courses are (probably) useful to some wizards, but not to squibs.

The Kwikspell course literature comes with two testimonials.

Madam Z. Nettles of Topsham writes:
‘I had no memory for incantations and my potions were a family joke! Now, after a Kwikspell course, I am the centre of attention at parties and friends beg for the recipe of my Scintillation Solution!’
 

Warlock D. J. Prod of Didsbury says:
‘My wife used to sneer at my feeble charms but one month into your fabulous Kwikspell course I succeeded in turning her into a yak! Thank you, Kwikspell!’

_{^{Harry Potter and the Chamber of Secrets}}

and states that they're useful for witches and wizards whose magical abilities are poor.

Kwikspell is an all-new, fail-safe, quick-result, easy-learn course.
Hundreds of witches and wizards have benefited from the Kwikspell
method!”

_{^{Harry Potter and the Chamber of Secrets}}

Interestingly, D. J. Prod appears to have gone from zero to hero with Kwikspell, having gone from 'feeble at charms' to warlock. What we don't know is whether these testimonials are accurate, but it's notable that both quotes come from wizards with poor skills rather than (former) squibs.

Like most correspondence courses, they're probably most effective if you apply yourself and have some natural ability. JKR confirmed that Filch's course was utterly ineffective, but that doesn't mean that it doesn't work for everyone, just that it didn't work for him (presumably because no courses will help a squib to become magical).

Filch has carved himself a niche at Hogwarts and Arabella Figg
operates as Dumbledore’s liaison between the magical and Muggle
worlds. Neither of these characters can perform magic (Filch’s
Kwikspell course never worked), but they still function within the
wizarding world because they have access to certain magical objects
and creatures that can help them

_{^{J.K.Rowling Official Site -Extra Stuff SQUIBS}}

It's also worth mentioning that another of Kwikspell's courses ("Wallop the Wombat Revision Course") is recommended by the Ministry of Magic itself to those who fail to achieve a passing grade in their W.O.M.B.A.T. tests. It seems highly unlikely that the Ministry would suggest people take courses from a company that offers courses that are known to be worthless scams.

(Do not be disheartened. You have only narrowly failed this most
demanding examination, and with a little further study would be sure
to pass. You are to be congratulated on a good attempt. We recommend a
crammer course of evening classes. Send an owl for full details of the
Wallop the Wombat Revision Course, available from the Kwikspell
Company.

_{^{HP: Lexicon - WOMBAT Tests}}

Additionally, we have evidence (from JKR herself) that other "correspondence courses" are effective in teaching inexperienced wizards and witches.

Occasionally, too, the magical community in a given country is tiny or far-flung and correspondence courses have been found a more cost-effective means of educating the young.

_{^{Wizarding Schools - Pottermore}}

As to how the course actually functions, we learn in the Gameboy Colour game Harry Potter and the Chamber of Secrets that lesson #1 of the Kwikspell course ("Learn Magic Fast with Kwikspell!") covers

• 
  The appropriate way to hold your wand


• The incantation for the Skurge (scouring) charm.

Which strongly suggests that the course comprises of one basic wizarding technique and one spell each lesson.

As I read it, Kwikspell is a borderline scam. It's on the same level as those ads you used to see in magazines, "Draw this [whatever]" to get you to send in for information on a correspondence art course. The course, in the end, is unlikely to actually teach you anything you couldn't learn as well for less money from books found in art stores and libraries -- but it will give you a "certificate" when you finish. The same is done for photography.

Sure, the MoM endorsed at least one of their courses, "Wallop the Wombat Revision Course" (thanks, Valorum, though I don't understand why anyone would want to wallop an innocent marsupial). This might be because the Ministry was misled into thinking the courses worked, bribed to give an endorsement -- or perhaps they actually did work for people with magical ability (which doesn't include Filch, as far as we know). The Kwikspell people surely didn't go out of their way to point out that a Squib wouldn't gain from sending them a lot of money.

In other words, Filch has been taken in by someone claiming they can teach magic to anyone, without even meeting them, for some number of knuts (or more likely galleons). He's sending off his money and getting "lessons" by owl, and almost certainly gaining nothing from it, other than a misplaced confidence that he will, in time, be able to use magic. We know he wasn't able to use magic, even up to the Battle of Hogwarts.

The only person in the books that we see using Kwikspell is Filch, and it doesn't seem to have helped him. For instance, in Order of the Phoenix Filch we have the following:

“Right you are, Headmistress!” wheezed Filch, who was a Squib and
could no more have Stunned the fireworks than swallowed them.

Apparently Filch was unable to do any magic at all despite the Kwikspell course.

However, it is unlikely that Kwikspell is meant for Squibs. It seems generally accepted that Squibs cannot gain the ability to do magic. For instance, we have Ron's comment in Deathly Hallows:

"But how are they supposed to have 'stolen' magic?" said Ron. "It's
mental, if you could steal magic there wouldn't be any Squibs, would
there?"

The opening paragraph of the Kwikspell course indeed seems addressed to wizards who are poor at magic, not those who have no magic at all:

Feel out of step in the world of modern magic? Find yourself making
excuses not to perform simple spells? Ever been taunted for your
woeful wandwork?

The testimonials as well reflect people who were able to do magic poorly, rather than not at all:

I had no memory for incantations and my potions were a family joke!

My wife used to sneer at my feeble charms

For such people it is certainly possible that Kwikspell would help. The first Kwikspell lesson is described as:

"Lesson One: Holding Your Wand (Some Useful Tips)"

Not holding a wand properly could easily be something that would contribute to a wizard's poor performance of magic, and useful tips on how to hold a wand is something that could address that and be taught in a correspondence course.

Therefore, while it is certainly possible that it is a scam, we have no particular reason to think that Kwikspell wouldn't work for those whom it was intended for.

Sounds like these "learn a language in 3 weeks" ads. Whether these work as bold as they claim probably depends on the person's abilities (memory, languagy affinity) and time invested. They probably teach basic techniques that will give people a head start compared to other methods.
It sounds that kwickspell is comparable, given the quotes are true. Certain techniques help people to make progress like how to memorize things etc.
"The appropriate way to hold your wand" seems one important basic technique that can make the difference - like they learn in Book1 about the important swish and flick for Wingardium leviosa.
But it sound that it is made for wizards/witches poor at magic but not squibs. That's why it doesn't work for Filch (though he obviously still hopes that there is some magic in him - like Neville told that his family already thought he'd be a squib, Book1?)