Exotics are even easier to get in year 2. You can buy them from xur but your best bet is to buy 3 of coins and use them when killing and ultra, you might spend 10 and get 2 or spend 40 and get 1 but easy exotics. To get past 300, you should do the normal raid and then the hard raid, or if you're pvp minded then iron banner or trials.

What light level are you? If you're 295+, you'd probably do well enough in Iron Banner (that's where I started out, anyway). If you reach rank 3, you'll get a package with a 310 artifact, and if you reach rank 5, you get another package with a 310 ghost, and am Iron Banner weapon or armor piece that will be 310+. Use SonicFusion's advice about the Three of Coins, especially once you hit 300. At 300, you have a chance of decoding an exotic engram into a 310 item, which you can then use or infuse it into your other gear, and once you hit 311, all your exotic engrams will decode at 310 (although I think they said that level will actually potentially go up to 335 once the update drops). My characters are all 311+, and I still haven't done the King's Fall raid. It was all through Iron Banner and Sparrow Racing (which I hope comes back soon).