To upload a completely new document
Go to the corresponding folder (e. g. Writer > To Be Updated to LO3.4). In the green bar above the list with the files there is a menu entry called "Add new..." with a arrow pointing downwards on its right side and in its menu select "File". Click on this entry and then chose "Document". Give a name, enter a short description, browse to the correct file on your computer and when everything is filled in to your satisfaction click on "Save". That's all.
Additionally, if you have not already done this (which is unlikely), your file should be named as follows NameOfTheChapter_INITIALS_date_.odt. The date format is YYYYDDMM. (e.g., uploads today should have 20120118) Also, if you are reviewing someone else's chapter, you would put your initials after the author's initials with underlining before and after your initials. (ChapterName_JS_DL_20120118.odt says that JS wrote "Chapter Name", DL reviewed it, and it was uploaded today.
To mark the file as being worked on
You go into the folder, click on the document name that you want to edit. In the green menu bar above there is a menu entry called "Actions". Click here and select "Check out". This will automatically create a "working copy" (and you will see a double entry for this chapter!) The original entry gets an extra banner, saying that XYZ has created a working copy on this date...
Don't forget to download the chapter. :)