What the Supreme Court appears to be doing in relation to Alice is applying copyright principles to patent subject matter eligibility analysis. Whether or not this was the intent, it has the effect of "promoting the Progress of Science and useful Arts" by enforcing proportionality between contribution to society on the one hand, and scope of patent protection on the other.
One immediate takeaway is that clever wordsmithing will no longer carry the day. The courts, and hopefully the patent office, will now focus on the underlying inventive subject matter. Under Alice, if the underlying idea being claimed is old or well-known, or the claims are worded to cover essentially all embodiments of the idea, then the claims should be deemed to recite ineligible subject matter.
Another takeaway is that we have a further rationale for ignoring recitation of post-solution activity. Claiming the computerization of a known process, and then adding a limitation such as "displaying to a user" will not convert patent ineligible subject matter into patent eligible subject matter.
What can be done to comply with Alice?