Once you've downloaded and installed Send to Kindle, you can activate the app in several different ways. First, you can right-click a document in the Finder and choose the Send to Kindle option near the bottom of the menu.
You can choose Send to Kindle from the Printer menu in any program that has one (here's Word):
Finally, you can click the Send to Kindle icon on the dock or drag a document to the Send to Kindle icon directly.
Whichever method you choose, you'll see the Send to Kindle's window in which you can specify a new title for the document and choose which Kindle you want to send the document to. You will also specify whether you want to use free Wifi or incur extra charges by using Amazon's Whispernet service.
If you check "Archive document in your Kindle Library" (which is on by default), your document will be available in the Kindle cloud, and thus to all of your Kindle devices. You can even deselect a device and send your document only to the cloud.
FormatNotice at the bottom of the window that you'll be advised about which format your document will be converted to. If you right-click or drag and drop, Send to Kindle will convert Word, text, and RTF to Kindle format, and preliminary testing seems to indicate that it uses the same KindleGen algorithms that are used by Kindle Previewer and KDP. If you right-click or drag and drop a PDF file, you'll have the option (in the aptly named Options panel) to convert the PDF to Kindle format. I tested some simple documents, and it seemed to work quite well.
If you use the print option, it will always send the document as a PDF, and the PDF cannot be converted to Kindle format. Note that the PDF document will be much larger than the Kindle version.
All in all, the Send to Kindle app looks like a useful tool for getting documents into your Kindle. The Send to Kindle documentation has a few more details.