Modules you'll need:
Install the WYSIWYG as instructed with CKEditor support. Enable the Media module and the dependency on File Styles. Under Configuration > Content authoring > WYSIWYG, Edit the text format of your choice. Under the Buttons and Plugins fieldset, make sure you select the Media browser checkbox. Hit Save.
Under Configure > Content authoring > Text formats, and click configure under the text format of your choice. Select the Converts Media tags to Markup checkbox.
Now, under Limit allowed HTML tags fieldset, add the img tag.
When creating a post, you'll now have an Add Media button. Select the file you want to upload and click Submit.