To share, hit the Share button in the upper right corner of a completed document to open the Share Settings dialog.
Each document has a unique link for collaboration, which you can find here or in the toolbar of your web browser.
Under the Who has access menu, select Change next to the first option to be taken to another dialog.
These are your visibility options. The default setting for all documents is Private, which means even if you share the link to the document with other people, no one will have access to it unless you have explicitly granted them permission under the Who has access menu. Choose the visibility level that you want and a little something called "Access" will appear in the bottom of the dialog:
We will return to this shortly.
After changing the visibility options you can copy/paste the link to the document from your browser and share it with anyone to give them access to the document. You can reset visibility to private any time to cut off access to the document for people with the link. If you choose Public on the web, the document will appear in search engines, though I'm not sure how Google determines keywords from your document.
The only exceptions to the private option are yourself and anyone you explicitly grant permission to in the Who has access menu. The person must have a Google account to gain such permissions, and only you can control who gets permission. For these people, the document will appear on their own Drive home page in the Shared with me folder.
Additionally, you can choose whether to grant these people permission to edit the document and/or comment on it. This is what the "Access" option mentioned earlier is for. If you really want to, you can create a document that anyone on the internet can comment on or even edit without permission. Be cautious of which option you choose; enabling comments is about as far as you should normally go.
Last but not least, by granting others permission to comment or edit your document, you can collaborate on the document in real-time with those people. This is a highly useful feature for crowdsourced editing and use in the classroom. Docs always lists those viewing the document in the upper right corner, under Share, and their cursors on the page itself. You can communicate with others via chat by clicking the viewing list when it appears.
Before these share features, the only way to share a document was to publish it as a webpage. This option still exists, and is useful for copyrighting your work by giving it a publication date. Select it from the File Menu. For copyrighting, do not enable updating to the webpage; just publish it as-is and let it sit unedited from then on. If you intend to let others view the webpage, know that it currently does not display the document the way it appears in the editor, i.e. with margins and the like.
One more thing: you can share your styles and import other styles through the Drive template network at drive.google.com/templates. I haven't imported and exported many templates so I'm not entirely an expert. More on this in the future.
That about covers it for the most significant features of Docs. If anyone has any specific features that they want to know about, please put it in the comments section and I will update the tutorial promptly.