If you're an Evernote Premium user, you can configure individual notebooks to be accessible offline, whether you have an Internet connection or not. In your device's Evernote Settings panel under the Offline Notebooks option, just select the notebooks you want to keep stored on your phone or tablet.
Access note history (Premium only)
If you tend to revise notes over and over--or share them with other people--having access to older versions of your documents can be a lifesaver, should something critical get changed or deleted. Premium account users can access older versions of notes by logging in to Evernote on the Web, clicking the note attributes drop-down arrow for an entry, and then clicking View note history. A list of archived notes and their timestamps will appear.
One important caveat: Evernote does not save a copy of every version of every note, but rather makes a backup of your notes on a schedule that runs every few hours. If you make multiple changes to a note over a short amount of time, only the most recent version is likely to be saved. Don't rely on note history to save you if you accidentally erase your entire document 10 minutes after you create it.
Archive webpages, in whole or in part
Emailing a webpage or its URL to yourself for later retrieval never seems to work right. This task is especially difficult if you're trying to save a password-protected webpage or a news story that may simply vanish at a later date.
Evernote's Web Clipper lets you copy webpages in full to Evernote, but power users know that you don't have to grab the entire screen. When you use Web Clipper, it will automatically attempt to determine where the "meat" of a webpage is, encircling it in a yellow border and graying out the detritus. Use the arrow keys on your keyboard to grab more of the page (Up Arrow) or less of the page (Down Arrow), or to pick a different selection on the page (Left or Right Arrow). When you're done, press Enter to finalize your clipping and save it.
Master Evernote's search tool
Evernote has search tags and much more to help you unearth your best notes.
As your Evernote database begins to fill up, you'll have to rely more and more on searches to find what you're looking for. You can search for simple keywords, but this tactic will start to turn up a larger number of results, especially if you tend to use Evernote to save lots of information about a narrow set of topics.
Fortunately, Evernote's search system offers an advanced syntax that gives you more control over how you search your notes. Here's a quick guide. (You can dig deeper on this blog post or at Evernote's official Knowledge Base entry.)
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