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I use the latest new module (1.2) which has better permission features. I recommend you download and install it.
Using that, go to the 'Submit\Approve Permissions' section of the module in system admin and check the boxes in the 'Submit Permissions' section for registered and\or anonymous users to be able to submit news to one or all of your catergories. Only do one section at a time though - I noticed if you try to do all of them it only saves one.
Then, in the preferences section of the module, tick the 'Yes' box where it says 'Auto approve news stories without admin intervention?'. This allows a user to submit news without you having to approve it. However, you may want to ensure your users know (by using FAQ perhaps) that they have to tick the 'Approve' box at the bottom of their news article, otherwise it still won't show up. Bummer! That is what I have done anyway. If there is a way round it I'd love to know.
Good luck