I have 1 TB hard disk installed in my laptop on which I have installed windows. Now I have 450 GB remaining in my hard disk. I'm planning to install ubuntu 14.04. So I just want to know how the partitioning should be done. I mean how much space has to be allocated for root,home and swap directories.
For the root-partition 30 GB will be enough.
For the swap-partition choose the size just a bit bigger than your physical memory (RAM).
The size for the home-partition is really up to you, you may use the rest of disk-space for it. But this is really a matter of taste.
In Windows, open Disk Management, and shrink your main partition by however much you want to leave for Ubuntu. Leave it as unallocated.
Next, boot the Ubuntu install media, and tell it to "install alongside Windows". It will automatically install to the uncallocated space, and take care of creating the swap partition for you.
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It's not clear that how many partitions you have in your system! If you have only 1 primary partition and in that partition you've installed windows and 450GB space remaining in that partition then first you've to create another extended partition using that space! And slice that partition into 2 partition one for your ubuntu system and another for your ubuntu swap partition.
Then boot up ubuntu DVD. Install system select partition as other then choose / for the ubuntu partition and choose swap for the swap partition then continue! I'm in mobile if I go on pc I'll edit my answer in detail if you don't know how to do it.