In addition to the notes from @Ubiquitous, I'd recommend these excellent and free/open resources from a number of academics. These are all posted freely and openly by the authors, and are all high-quality (and all at the "graduate level").
Cochrane's monograph should be your first stop for time series, period. Stachurski covers some of the very cool theory behind 'metrics. Creel provides a very nice, slide-style set of notes -- gives you a chance to "quickly peruse" graduate econometric theory (as well as very cool parallel computation estimators). Train has nice chapters on simulation-based estimators. Hansen is an all-around textbook with reasonable depth.
Somewhat further afield, but perhaps useful for the intro level, are the "Think X" series of books from Green Tea Press:
These are truly intro-level books -- and very excellent as such. I use the "Train Problem/German Tank Problem" from Think Bayes whenever I need to illustrate the usefulness/intuition of Bayesian approaches to a beginner.
I will note that for self-study, Hayashi (noted in another answer) has a lot to offer.
Edit: If you are looking for broad examples of methodologies, I would strongly recommend "Mostly Harmless Econometrics." The book has a particular focus and mild methodology bias (see Andrew Gelman's nice review, which points out some of the topics missing), but it is still excellent at diving directly into application of their ideas, via examples from the literature and replication. I strongly believe that replication is key for learning about research methods, so I like their approach quite a lot. One minor warning: to get to the applications, you have to get through their very long intro chapter on the basic of regression. But hang in there -- that chapter is great as well, and you'll then get to enjoy the fruits of application/replication after it.
Also, if you want to know a little more about what economists do, check out these two non-technical books: "Passion and Craft" and "Lives of the Laureates." ("The making of an economist, redux," is also good, but perhaps less ...exciting of a read. Take that for what its worth, since the first two books aren't necessarily action page turners.)
Edit 2: as @cc7768 notes in the comments, John Stachurski and Tom Sargent's website, QuantEcon, is absolutely fantastic. They essentially work through the major basic concepts you need for computational economics (and so many things are computational these days), and give you clear, working code examples for a vast number or major problem-types. You should very definitely check it out if you are interested in economic methodologies -- it's probably the first place I'd recommend you stop, actually. Very easy way to dip your feet into serious methodology examples. I learned an enormous amount from early versions of these notes.