I, too, am experiencing this problem. It occurs with both Safari and Firefox. It wasn't bad at the start; occasionally what seemed like my internet would cut out while I was surfing, but then the problem began to last for longer durations. As of this morning, I've been trying to get Safari to open for two hours with no success.
Here's the specifics. I open Safari. Most times, the load bar will extend about 1/6 the length and stop, displaying my homepage address in the address bar. Sometimes, the load bar will creep halfway, and part of my homepage will appear; typically, images don't load, and sometimes the page format gets wonky. Rarely, the homepage will fully load! I can even move through the homepage's image slideshow seamlessly. However, if I try to go to another page, I'm back at the 1/6 occurrence. Very rarely, everything works fine. Closing the laptop or Quitting Safari kills the connection, and I have to start this stupid process all over again. Finally, Firefox is either all or nothing; either the pages load and work fine, or nothing works at all.
I've done a DNS manual adjustment, I've created a specific Network, I've unchecked Safari from the iCloud options, I've run scans for malware and viruses (and came out clean), and I've done a clean reinstall of Yosemite. There's no need for me to tweak my router or contact my ISP; every other wireless application in our house is functioning perfectly. It's not the wifi.
Nothing's working, and I'm about to throw my computer out a window (not really, just frustrated). Any help would be so very appreciated.