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When you're looking at a ticket page, you could also check to see if the patch is marked as "merged" in some in-progress new version of Sage. Once a ticket is marked as "fixed", this tends to happen pretty fast and you can just install the new version (even if it's a development version).

As to why you would want to unapply a patch, this is useful if you're using multiple patches at once, which possibly conflict with eachother (i.e. one can't be applied after the other). Or if you depend on your Sage install for something critical which you don't want to inadvertently bring bugs into, but you also want to use Sage for some other non-critical task where you don't care about unreviewed patches. So maybe none of these matter to you, but you might want to keep the possibility in the back of your mind.

And it bears mentioning that many of the nice folks here are the same people having opaque discussions on Trac! It's just a matter of context :)

Lastly, you're right that it would be more intuitive and useful to have the instructions for applying a patch separated in the manual from the instructions for reviewing a patch. In fact, you can make this happen! To do it, just read the other sections on contributing to Sage, open a ticket and submit your patch. Feel free to add me ("niles" on Trac) to the Cc field of the ticket if you'd like me to take a look at it with you. The same probably goes for @Volker Braun and @kcrisman, so don't be shy about adding them too.

When you're looking at a ticket page, you could also check to see if the patch is marked as "merged" in some in-progress new version of Sage. Once a ticket is marked as "fixed", this tends to happen pretty fast and you can just install the new version (even if it's a development version).

As to why you would want to unapply a patch, this is useful if you're using multiple patches at once, which possibly conflict with eachother (i.e. one can't be applied after the other). Or if you depend on your Sage install for something critical which you don't want to inadvertently bring bugs into, but you also want to use Sage for some other non-critical task where you don't care about unreviewed patches. So maybe none of these matter to you, but you might want to keep the possibility in the back of your mind.

Spkg's are something different from patches, and instructions for installing them are given in answer to a different Ask Sage question.

And it bears mentioning that many of the nice folks here are the same people having opaque discussions on Trac! It's just a matter of context :)

Lastly, you're right that it would be more intuitive and useful to have the instructions for applying a patch separated in the manual from the instructions for reviewing a patch. In fact, you can make this happen! To do it, just read the other sections on contributing to Sage, open a ticket and submit your patch. Feel free to add me ("niles" on Trac) to the Cc field of the ticket if you'd like me to take a look at it with you. The same probably goes for @Volker Braun and @kcrisman, so don't be shy about adding them too.