My response might be colored by my experiences at the school I teach at (most of my students come from a poorly-funded, poorly-managed public school system), and this is going to be heavy on the "skills" part of your question, but here are the things that I frequently find myself wishing students had been taught before they got to my class:
How to write a decent essay. This is the single most important skill a history student needs. Really, it's mickey mouse stuff, but for some reason a lot of my students never seem to have been taught this, or seem to have forgotten how to do it the moment they graduated high school. They need to learn how to craft a thesis statement, a good introduction, how to structure paragraphs so that each one has a topic sentence and focuses on one point/subject/piece of evidence, how to put those paragraphs in an order which makes sense, and how to tie it all together in the conclusion. My students tend to get hung up on trying to figure out the "right" answer to my essay questions, while struggling to express themselves well - when all I really want is to see them make a compelling, rational argument and be able to point to evidence that backs up their point of view.
How to cite things. Obviously every school/subject has its own peculiarities when it comes to citing stuff - so i don't expect everyone to have the entire Chicago Manual of Style or MLA handbook memorized. But they should have a rough idea of where to look to figure out how things should be cited, and an understanding of what kinds of basic information need to be in a citation. Most importantly, they need to understand when citations are necessary. Too many students quote or copy without attribution these days.
That Plagiarism is Really, Really Bad. Kind of related to the above point, and again, kind of mickey mouse. But way more common than it should be.
How to do historical research. I would love it if more of my students came into my class with a better understanding of what the differences between a primary and secondary document are, and how they can be analyzed/critiqued/compared to create a more complete and more balanced view of the past. Too many of my students think that it's good enough to find one source that "proves" their point, when there are countless other sources out there that would support the opposite conclusion. Obviously critical/comparative reading is one of the skills that I'm supposed to be teaching them too - but I often feel like I need to start at a much more basic level that I really ought to (ie: "in what ways might this collection of primary documents be a better source for us to use than this wikipedia article written by god knows who?" or "why might we not want to trust everything that's written in an autobiography?")
How to use their library. This one is near and dear to my heart. We live in a time of marvelous new technologies that make historical research so, so much easier than in the past - there are digital tools, catalogues, and databases out there that can bring countless resources to bear on virtually any history assignment. As someone who uses and relies on those resources daily I always find it shocking how many of my students end up trying to do their assignments without using JSTOR, without making use of the huge databases of primary sources that are out there, or without even checking a book out of the library. It's a crying shame that so many resources can go so untapped by otherwise bright students - a lot of the people in my classes really needed a better grounding/introduction to the basics of using a catalog, finding the right database, etc. And the first thing that I always drill into their heads is that they should always ask a librarian for help - my school employs a whole staff of powerful wizard-people who can work magic as librarians, but their skills are chronically under-utilized by students.
In addition to what the awesomely named /u/AnacreonInHeaven said, I would also add:
Critical Reading. It seems that a growing number underclassmen were not taught how to pick out the important bits from an article or source. One of the most common complaints I get from my students is that they don't know what matters in the readings my professor assigns because the important bits aren't conveniently put in boldface type. The result is that they get confused and frustrated early and often.
The Concept of Historical Interpretation and Historiography. While K-12 history is largely geared towards installing information into young brains, that's not really how academic history works. Sure, you learn stuff all the time, but a lot of history is, frankly, people trying to put together an explanation - explanations that can be overturned and discarded by a different explanation. The fact that even authoritative-seeming textbooks can be wrong or biased is an important realization to have early on.