In the "Post Reply" window look in the bottom left for a green cross and the description "Add Attachments" - click that link.
This pops up a second window titled "File Chooser" with a green button in the upper left that says "Upload Files" - click that button and select the files you want to upload.
Once it is done uploading a check box will appear on the same "File Chooser" window that says "Insert all photos and videos into post body (large size)" which allows for easy insertion of the now-uploaded pictures into your post.
I'm looking forward to seeing your pictures, sounds like a great experience.