Most people I know only make one, maybe two overseas trips during their PhD (usually to the largest/most prestigious conference in their field). Some research councils offer funding, but this normally only forms part of the cost. If the conference is large, there is sometimes a travel grant system in place, but again this will cover only some of the costs.
My Uni has a scheme where a certain amount of money is available per research student per year of the PhD for travel(I think it's 350), and more can be found if the student acts to promote the research institute in other ways (I'm the postgrad rep and organise the annual conference), and I pretty much rely on this and self-funding. Off to San Francisco in March, my uni has covered the flights and registration fee, I cover the hotel, and received a travel grant for the conf.