Guide for using all the tools and kits
I can't seem to find this information in the three main rule books, but outside of some general information about lock picking, is there a definitive guide for how to use the various tools and kits with which a character can become proficient? I'm looking mainly for what skill or ability checks can be made with them, general modifiers and what sorts of tasks can be performed. Without that, they seem more fluff than substance.
I've seen some similar questions here, but usually directed toward a particular kit rather than a general overview. Is there a source written in any official rulebooks?
Can there be a *definitive* guide for an open-ended system that new supplements and adventures are still being released for?
Since this question was asked and answered, Wizards of the Coast has published Xanathar's Guide to Everything. Among the many additions and clarifications, pages 78-85 give a very detailed treatment on how to use all tool kits and what can be gained by proficiency with them.
It explains the difference between a skill proficiency and a tool proficiency, as well as how they can work together to accomplish specific tasks that would be more difficult or impossible without them. Each tool has a number of skill synergies which are used as an example and guide for the DM, as well as a table of common DCs for various tasks one might use them for. These are well thought out, listing activities that might actually have a use in play, such as using Alchemist's Supplies to produce a puff of thick smoke.
It is notable that the DCs listed don't necessarily require the tool itself, but that proficiency in them might allow a character to perform a task that would be normally impossible or more difficult for the unproficient character. For example, a character with proficiency in Brewer's supplies might allow one to detect poison in a drink
In addition, it lists the components for each tool, so that players and DMs can have an idea of the items actually at their disposal.
Like everything else in the Guide, the rules are optional (the text calls them "advice"), but they do provide a wealth of detail where before there were only the most general of guidelines.
You did mention it, but I think it should be emphasized that the activities listed in XGtE are examples and in no way are meant to be exhaustive. Great self answer.