Until iOS can fully replace your computer, it's going to have to gain a lot in terms of capabilities. Luckily, with each update to the operating system, more and more of those much-needed features are added. One such feature is the ability to upload photos to a Web site through Mobile Safari.
The process and workflow is identical to what you're used to when using a computer, but it's been adapted to iOS.
Using Tumblr as an example, when you want to upload a photo, tap on the Upload button and then select if you want to take a new photo or use one from the Photo Library.
From there, depending on the Web site, the photo will automatically be uploaded (as was the case with Tumblr) or you'll have to initiate the upload.
Unfortunately, you're going to be limited to uploading only photos. With iOS not having a public file management system built into it, it's not surprising, but it would be nice to be able to access your files through an app such as Dropbox. Maybe in iOS 7.
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