I have a Raspberry pi 2 model B with an sd card Raspbian on it. I have set up an SSH connection through putty. I'm new to this. So how do I launch Raspbian. I know that I can't use startx. Please help
If you have successfully used putty to log in (user = pi, password = raspberry), then you are already in raspbian. And that means that you already know the IP address of your pi. If you are looking for a GUI then @dastaan 's comment is correct, but you will first have to log into the command line via putty and install / enable vnc - look here for a guide.
If you have not successfully logged in via putty the you have a different issue, made more or less complex depending on whether you are planning on using wifi or a cable to connect the pi to you home network.
If you are going to use wifi, realistically you'll need a monitor and keyboard so you can boot the pi up into the console and use the command line to set up wifi (and vnc server for that matter). There are many guides out there, just google "set up raspberry pi wifi command line".
If you are using a wired connection but can't figure out how to ssh using putty, then your issue is probably that you don't know the IP. You can use a smartphone app like fing (I love that app) to find out what IP has been assigned to your pi. Or you can hook the pi up to a monitor and look at the boot messages, which include the assigned IP address (looks like xxx.xxx.xxx.xxx). Then use putty to ssh to that ip address and follow the vnc guide mentioned above to install vnc server.
Very important, you should have installed raspbian, not NOOBS. If you installed NOOBS you still need to install raspbian, which is done by hooking a keyboard and monitor to the pi and walking through the install instructions.
Hope that helps. Let me know if you have questions.