TL;DR Things like CC0, Unlicense and WTFL create unexpeced legal hazards in some jurisdictions. The MIT License does not really put anything in the public domain, but it the safest license to use if you want to offer your stuff with as few restrictions as possible in a world-wide setting. In the USA, CC0 can be used, but I do not recommend it for software.
Why is this [to place software in the public domain] difficult?
The difficulty of placing software in the public domain in the public domain is closely related to something called "moral rights" that originated as civil law in the Napoleonic Code (1804, France) under the name of droit d’auteur (literally: author's rights).
Jurisdictions with strong moral rights have a tradition of making it near impossible to dedicate anything to the public domain.
Moral rights include the right of attribution, and the right of integrity (but the exact list of exactly what is protected by moral rights varies between jurisdictions).
In the Norwegian copyright act, moral rights are described in the first parts of § 3, while the third part says that these rights cannot be waived. Here is a direct quote (translated by me):
The author may not waive his rights under the first and second paragraphs, unless the use of the work in question is limited in nature and extent.
The "limited in nature and extent" addendum allows ghostwriting.
However part four states than under no circumstances can the right of integrity be waived. Quote (translated by me):
This right may not be waived by the author.
To compound the problem, moral rights are forever in Norway. In Germany, an author can commit suicide and then wait for 70 years to dedicate his works to the public domain. In Norway (and a few other countries in northern Europe), this option is not available.
how can I release some project effectively into the public domain, for jurisdictions that have such a concept?
I do not think that this is possible for all jurisdictions.
The most professional (as in: written by lawyers, not kids) attempt to create a legal tool to enable authors to dedicate their work to the public domain is CC0.
IMNSHO, while well intended, it fails, and its use creates a legal hazard in several jurisdictions (including Norway, where I live).
OSI seems to think so as well. In 2012, CC0 was submitted to OSI for review. After facing harsh criticism, the application was withdrawn.
(One of better known legal hazards of CC0 is its infamous patent clause, which I discuss in this answer.)
Another license that is supposed to do this is the Unlicense. AFAIK, it has never been submitted to OSI for review, but if it had, I am pretty sure it would have been summarily rejected. OSI's co-founder Bruce Perens call the the Unlicense a "crayon license", adding:
The point is that such things have done serious harm to developers when
they've not behaved as expected in court. Thus, naïvely propagating one
could be considered to be in the category of irresponsible acts that can
Personally, I believe that it is unrealistic to aim for the "public domain" if your audience is world-wide. There are too many local quirks in copyright and a one-size-fits-all legal tool to put something in the "public domain" may have some totally unexpected (and harmful) side effects.
For instance, in Norway, publicly performing recorded music distributed under CC0 requires you to pay a levy to GRAMO (a collecting society monopoly authorized under the Department of Culture), but doing the same with music distributed under CC-BY is free. Yes, this consequence of the use of this license is totally absurd, but some copyright laws (at least in Norway) are.
My recommendation is to stay clear of anything with pretense to put anything in the public domain, as well as "crayon" licenses such as "WTFL" and "Unlicense".
A license that will put as few restrictions as possible on the use of your project, while not creating legal hazards for yourself and your users, is the MIT (aka. Expat) license.
The MIT license does not abandon moral rights. Since they're not mentioned, the jurisdiction's default civil law applies.
The MIT license is also much more aligned with a "traditional" take on copyright. If you use the MIT license, authorship is not abandoned, but specific (normally reserved) rights are explicitly licensed to the licensee. This model fits much better into the legal framework of civil law jurisdictions than the much less conventional public domain dedications that is the gist of CC0, WTFPL and Unlicense.
If it varies greatly per jurisdiction, how can I do it for the US?
In a localized case, including the US, there is usually some recognized way to do this.
As for USA, you may consider using CC0 if you don't mind having your downstream recipients worry about submarine-patents. It was written by US lawyers, and it fits the legal situation in the USA to a tee - but it is really for artistic and literary works. IMNSHO, it should not be used for software.
Let me add that I think CC0 is pretty safe way of putting something in the public domain in common law jurisdictions, but much less safe to use in civil law jurisdictions.