Your photos are shown in your photostream, which will be at flickr.com/photos/username (where "username" is the identity you've chosen). Here's mine.
You can also maintain a profile page, to tell other Flickr users about yourself. This is at flickr.com/people/username. You can go wild and tell the world everything about yourself; or you can keep things strictly anonymous. Here's mine.
Every other Flickr user is potentially one of your Contacts. Photos from your Contacts are automatically aggregated on to a page customized just for you (it's at flickr.com/photos/username/friends). This is a quick and easy way to keep track of new additions to Flickr from a large number of people. To add someone to your contacts list, just hover your pointer over their Buddy Icon, the little square image that appears next to their username. Buddy Icons appear everywhere in Flickr; they're a great way of noticing people and remembering who's who.
Every photo in Flickr can have notes (like annotations) and tags (words descriptive of the content or style) added to them, by the person who uploaded them and by anyone else. Your photos remain your own, but other people can add metadata to them. This is a very important part of the service, because it's one way that the social aspect of Flickr starts to shine.
Any photo can be added to a group as well. Groups exist to cover all kinds of crazy photographic ideas and much more besides: the squared circle group is hugely popular; perhaps you'd like to tell the world what's in your bag or even what's really in your bag; JPG Magazine's 1 photo a day - no borders please is a constantly engaging place to hang out; readers of Mac DevCenter will probably enjoy the Macintosh group; and for something really unusual, how about piles of books or boring photos?
You can join a group, or create your own. Adding a photo to a group effectively adds metadata to it. The image remains in your photostream (and adding to a group does not affect your bandwidth quota on free accounts) and still has the same tags and notes you've added; but now it also appears in the group's photostream (known as a "pool") as well.
Most views you see in Flickr (your photostream, your contacts, group pools) have their own syndication feed in RSS and Atom formats. This creates yet another way to view photos, using any compatible feed aggregator such as NetNewsWire or Bloglines.
Uploadr and 1001
The basic Flickr upload page has the kind of upload interface you'd expect to see in a browser.
But there's also a handy bookmarklet which works with most Mac browsers. From any web page, you can click the bookmarklet and it will refresh with a simple display of all the images it found. Click the one you wish to add to your photostream, and it's done.
Flickr's own Uploadr software is available for OS X. It's free and very simple to use. After downloading the disk image (a Flickr account is required for entry), expanding it, and dragging the application to your hard disk, all you have to do is enter your user details in the Prefs panel, drag in some pics, and click "Upload." As they say round here, it does what it says on the tin.
Once you've clicked Upload, you'll be shown a sheet where you can pick the privacy setting for this image, and add some tags to it.
What the Uploadr doesn't offer is anything in the way of image-editing tools; you can't rotate, resize, or make any other changes to the image itself. It's not an editr, it's an uploadr.
1001 is a third-part uploading tool for OS X, which takes things one step further than the official Uploadr.
As well as offering all the upload functionality in the Uploadr, 1001 also helps you to keep a watchful eye on the photostreams you've added as contacts, and the groups you have joined.
New pictures from these subscriptions are automatically displayed by 1001 in a neat little alert window which you can leave open all the time. Optionally, you can use 1001's Dock icon space to display new images too.
Both the Uploadr and 1001 are currently in beta, which means we can expect more from each of them in future. Both are perfectly usable and stable despite the beta status, and are excellent ways of getting a photo online when you're in a hurry.