I did a bit of research online for you - the quick answer is, your camera does not have a filter thread (meaning you cannot screw in filters that you can normally buy from a photography store.)
The long answer is this - the following is quoted from a flickr discussion I found, these words are not my own, but I have verified that it is accurate.
The lens has what is called a bayonet mount, which does not by itself fit any filters. You will need an adapter ring to fit filters on the camera and hence your filter size depends on the adapter. Some of the really cheap ones on Amazon have negative reviews saying they don't fit well and the metal types seem to damage the bayonet mount, so be careful what you get. I have the Lensmate adapter for Canon SX10/10/30/40 and it works very well for my purposes. It fits 58 mm filters.
One thing to note: The lens cap that comes with the camera will no longer fit once you put the filter adapter on. If you plan on leaving it on the camera all the time, you will need to also buy a 58 mm lens cap. They're only five bucks or so.
Another thing to note: If you have a lens hood that fits the camera without adapter, it will no longer fit either once you put the adapter on. So you also may want to buy a 58 mm lens hood to fit the adapter if you use one.
Here is the link to the aforementioned adaptor you will need. http://www.lensmateonline.com/store/sx20sx10sx1.php
ALSO the following is from the same discussion
I use the Canon FA-DC67A adapter ring. It is specifically made for the SX30-IS and the SX40-HS. Once attached, you can use 67 mm filters.
The Canon one imo is more expensive but it is a genuine accessory for the camera. Personally, I would call Canon myself instead of camera stores if the people you talk to are not knowledgeable, Id Call Canon.
Here is the link to the Canon website and th link to the discussion.
Details on the Adaptor - http://www.canon.com/camera-museum/tech/report/2011/01/
The Discussion on flickr - http://www.flickr.com/groups/canonsx40hs/discuss/72157628218494185/
Check your manual for a refference page for the adaptor ring - the Model number you need should be there (as I have posted the model number, it may be different between regions.)
1) Olympus OM1 [Zuiko Auto-S 50mm f/1.8]
2) Pentax MZ-60 [Sigma 28-90 & 100-300]
3) Canon 7D [EF-S 15-85 & 70-200mm f/4 IS & 50mm f1.4]
4) Leica M [50mm Summicron Pre-aspherical - Silver]http://www.poetproductions.net