1. Buy a replacement power supply (But you would need to make sure you get the right size. The most common is ATX but with only 250watts I'm guessing you might have a small computer that might not be ATX. It could be micro ATX or another small case standard of some kind)
2. I think you would be a good candidate for a supplimental power supply. This is a power supply that fits into a 5.25" drive bay (The spot where you could add a DVD or BluRay drive). These are made by HIS, ThermalTake and I think Ultra makes one too. Basically it's a second power supply it can be used to power hard drives, fans or video cards (depending on the model). I used to have one. I worked great.
What is your specific PSU? The most important part for a GPU running off the mobo is the 12V rail power. Many high wattage PSUs have a lot of their power spread out... however, a 250W is pretty low and might not be good quality. You'll want at least a 20A 12V rail.
Ok looks like it only has a 14A 12V rail. Also, the 12v and 5v rails "do not exceed 218W". A typicall CPU is 100 - 130W depending on model and that sort of thing. The GT 240 I think is around 70-80W. It would be cutting it very close... and I doubt that it's a quality PSU. I recommend you find a decent but low priced 350W PSU.
Hmmm... I'll say that it is a risk. I've heard that exceeding the PSU limits can (if you're lucky) only melt the PSU but on the worst side of it, it will melt something in the PSU and cause a surge to the mobo which can easily take out the mobo, RAM, even CPU and vid cards...