The part of your question that matters here is
[how do] experienced Javascript developers ... get the basics of Javascript down in 24/28 hours
Experience is not something that you can get in one night, one week, one month, or one year. Experience is something that you acquire over the course of years of hard work — encountering bugs, learning best practices, re-writing code that you wrote four years before and asking yourself, "why did I do this", optimizing for far-less-than-perfect environments ...
That being said, if you have only one night to learn enough to make you dangerous, then start at the bottom and work your way up. Daniel Vassallo has given you one very nice link already, and more than one person has suggested W3Schools for a quick overview of both Javascript and the DOM.
But don't start with any of that. Instead, start by determining, as well as you can, what it is you want to be able to do with Javascript tomorrow. To do that you need to ask yourself two simple questions.
What is your level of programing expertise? Can you code complex algorithms in C
and C++
with the occasionally foray into some variant of assembler? Have you ever worked on a decently large project in a slightly "higher level" language like C#
or Java
? Do you know at least one scripting language decently? Or do the phrases "functional programing", "class-based inheritance" and "bubble sort" mean nothing to you right off the bat? If you are in any of the first three categories, a little time with a few of the better tutorials on the Internet, and maybe a quick look at a Stackoverflow question or two should have you up and running in no time. If you are in the last category, you might do well to start off with the basics of programing in general. No matter what you are going to need an environment in which to learn. Which brings us to the second question ...
What is your platform? Are you planning on doing some server-side programing with node.js? Maybe you planning on developing some utility in a Rhino or JScript environment? If either of these situations are the case then reading the documentation for the platform you will be developing on will stand you in much better stead than reading up on the DOM. If, on the other hand you are planning on developing for the web, then you cannot do much better than to grab Firefox with the Firebug extension and start by building a simplified version of what you are going to be working on tomorrow.
And if none of this is in any way helpful to you then hopefully by the time you have finished reading it, someone else will have answered the question in a far more suitable manner ... that's the beauty of Stackoverflow.