Bear comes with free browser extensions for Safari and Chrome, which allow you to save portions or entire web pages as Bear notes which a single click. The extensions are currently in beta and you can install them by following these instructions:
For Safari, Visit it's page on the Safari extension gallery and click on "install".
For Chrome: Visit the Bear's Chrome web store page and click on "Add to Chrome".
For Firefox: Visit this page on the Mozilla Add-ons site and click on "Add to Firefox".
Once installed, click on the Bear button and after a few seconds you'll see a new note appear inside Bear.app with the page main content. Select a portion of the page and click the Bear button. A new note with the selected informations will appear in Bear.app.
Through Safari/Chrome extensions preference panel you can access to some Bear options, which allow to add tags, import images and append the page url to the Bear note. On Chrome you have to click on "Options" near the Bear icon.