A solution of bleach and water, perhaps coupled with a good detergent. All the commercial mold and mildew remover products have good old bleach as their basic ingredient anyway, so you may as well mix your own and save money. I would try about a 10% bleach solution first, but it is likely you will have to go stronger, maybe twice that or even more. Use a soft bristle brush to work it into the fabric.
If it is canvas and it takes a lot of scrubbing to get it clean, you may have to re-waterproof it afterwards. Canvas waterproofing products are available at most outdoor stores, some Walmarts, and some hardware stores. It's not hard - just wipe or spray it on.
More info on waterproofing:
http://ezinearticles.com/?How-To-Waterproof-a-Canvas&id=87245
Here are some waterproofing products
http://www.rayandrain.com/Tents/tabid/296/List/1/CategoryID/2/Level/1/Default.aspx?SortField=EAN,ProductName
http://www.trek7.com/what-is-the-best-way-to/waterproof-fabric?gclid=COH50di2spsCFYaV7Qod3EotPg