To edit an image already on your page or post, click the image once. The image will turn blue, and two icons will appear in the upper left: a “landscape” icon and a universal red-circle-with-slash. Click the red circle to delete the image, or the landscape to open the Edit Image dialog box.
The pop-up editing box is organized differently from the information box that appears when you originally upload or insert an image. It’s straightforward to change an image’s alignment, or to edit the title, caption, alt text, or description. It is important to know, though, that your edits will only apply to this instance of the image. (They won’t be saved to the Media Library, so if you insert the image somewhere else, the original information will be inserted.) You can also change what it links to, though you need to know that “Link to Image” means link to the media file (not the attachment page.)
You can also change what the image links to, but the wording may be unfamiliar. “Link to Image” means “Link to Media File,” and there’s no option to link to the attachment page. If you need to do that, just delete your image and start over.
Image size, too, is different: you aren’t allowed to pick a different set size (thumbnail vs. medium or large). If you had inserted the medium size originally but now want the large version, delete the image and start over. If, however, the “large” size image for your site is a bit too large, though, you can use the scale to reduce it using the percent scale (don’t try to increase it — image quality will suffer noticeably).
Last, there is an Advanced Settings tab. This tab is, in fact, the only way to get to the settings here. They all relate to how this particular image is display in this particular location, and most of them require understanding a bit of CSS (the styling code of the web) to make full use of, but have a look and experiment if you’re curious, or see the Image Settings article from WordPress.com. (WordPress.com is different from the official WordPress codex, but it often has helpful articles that are relevant to users of both versions of WordPress.)