AFAIK there is no way in the GUI that editors can actually see the file size (in an out-of-the-box 7.5 installation).
You could view the public URL to a file by double-clicking it in media manager (which opens the image for editing), clicking the Options button and hovering over the Download This File link.
That way you can copy the link address. A bit cumbersome, though.
Both file size and url should be more easily available - you should post a feature request :-)
You could also get the url from the "globe" link (to view mode).
Regarding file size, you could check out this blog: https://episerverblog.wordpress.com/2014/06/11/displaying-file-size-for-your-mediadata/
What I did was adding a Size as a property of GenericMedia. Then on Saving and Creating event, I set the size. (If I remember correctly, one is called when the file is uploaded, the other one when the file is replaced, but it's been a while). However, this was used to display the link and the size next to it, not really what you are asking. If you need to display the size somewhere, this might be a good workaround.
Thanks for all answers!
I must say that it's a very strange decision by EPiServer to remove information about how big a file is. I think this is the first cms I've worked with that's not displaying that kind of information. I would say that filesize should always be visible and if the file is an image the image size should also be easy to view for the editors.
Update: OP has created a Feature Request for this. Linking it here for reference: http://world.episerver.com/forum/developer-forum/Feature-requests/Thread-Container/2015/8/make-it-possible-for-editors-to-see-file-size/ /Moderator
In EPiServer 7 the editors could easily see file size in the "files" tab. In EPi 7.5 under the "media" tab that information seems to be missing. So how can the editors find out the file size? Also is it possible to get the public url to a specific file?