First I should note that the ratio in Alice, while easy to state, is rather hard to apply. Many words have been shed trying to characterise precisely what Alice-style abstractness really is. But the reality is, unless high courts rule further on this, we're left with working it out as we go.
Nevertheless, I'm feeling brave, so I'll give it a go. For simplicity, all my quotes are from the headnote (though I note that this is not part of the opinion proper).
The holding of Alice is:
Because the claims are drawn to a patent-ineligible abstract idea,
they are not patent eligible under §101.
This provides a concise statement. The claimed invention must not relate to an abstract idea.
But "abstract" is not defined anywhere. Instead, the majority indirectly characterises it, with reference to Mayo.
In applying the §101 exception, this Court must distinguish patents that claim the "buildin[g] block[s]" of human ingenuity, which are ineligible for patent protection, from those that integrate the building blocks into something more.
This approach is somewhat formalised:
Using this framework, the Court must first determine whether the claims at issue are directed to a patent-ineligible concept. If so, the Court then asks whether the claim's elements, considered both individually and "as an ordered combination," "transform the nature of the claim" into a patent-eligible application.
The majority apply this approach to the subject patent:
The claims at issue are directed to a patent-ineligible concept: the abstract idea of intermediated settlement.
Viewed as a whole, these method claims simply recite the concept of intermediated settlement as performed by a generic computer. They do not, for example, purport to improve the functioning of the computer itself or effect an improvement in any other technology or technical field. An instruction to apply the abstract idea of intermediated settlement using some unspecified, generic computer is not "enough" to transform the abstract idea into a patent-eligible invention.
Should applications be phrased differently?
No. Or at least, not without something more:
This Court has long "warn[ed] . . . against" interpreting §101 "in ways that make patent eligibility 'depend simply on the draftsman's art.'"
And this seems right. The substance of the claim is what matters, not that it uses any magic words.
So, how does one approach this in practice?
It seems to me that you simply have to ask: what really is the point of the invention?
If the point of the invention is a method of trading securities (which is embodied on a computer), it seems that that is a fundamentally abstract idea: you're not claiming anything technological, you're just claiming a fundamental building block of business.
However, if your method is faster for computers to perform than prior art methods which have the same aim, then this is more than abstract. The point of your invention is no longer just business, but better technology. So while the overall concept may well still be abstract in general, at least some features improve the function of a computer such that the invention is transformed into a patent-eligible invention.
What inventions should be kept as trade secrets?
If your invention really doesn't do anything particularly technical, you should probably keep it a secret: it's likely to be abstract and patent-ineligible.
A digression on comparative patent law
Though there is no mention, even implicitly, of a desire to align the US with the European approach, it seems to me that there are some clear parallels between Alice requirement for non-abstractness and the European requirement for a technical effect. That is, for an invention to be patentable in Europe, the novel features must have some technical effect: the effect of the invention cannot solely be non-technical, such as a better business method, and the technical effect cannot solely be from well-known features like a general purpose computer.
This seems to me to generally be saying the same thing as the US approach, but with different words. But as far as I know, there have been no formal studies into the similarity between the two approaches, so this is nothing more than idle speculation.