Are you able to physically connect both hard drives in the same machine? If so, great, the steps are easy. I'll outline each one, and you may ask for details for each if you are unsure about them.
1 - Connect the new drive, disconnect the old one. Install Windows from DVD as you would in a clean, fresh machine.
2 - Once Windows is installed and working fine, power off and connect the old hard drive.
3 - Boot using Ubuntu Live CD
4 - Start
gparted, shrink the Windows partition to make room for Ubuntu. I suggest shrinking to the minimum size plus approx 15/20GB. Create an extended partition to take up the all the remaining space
5 - Copy the Ubuntu partition from the old to the new drive, inside the extended partition. Copy the
swap partition too, if you have one. Yes, gparted can copy and paste partitions from one drive to the other ;)
6 - You may resize the Ubuntu partition a few gigs, but I suggest leaving room for a brand new NTFS "data" partition, which in the future can be used by both systems to store your music, videos, documents, downloads, etc.
6.5 - Also, if you don't have a
swap partition yet, create or leave room for one. Size should be at least equal to your RAM, to enable hibernation.
7 - You now should have these partitions: 2 primary ones created by Windows (a 100MB one and the shrank one, ~30GB), an extended partition taking the rest of the disk, the Ubuntu logical partition inside it (~30GB too), the swap, and a lot of free space (or your newly-created NTFS "data" partition). Label those partitions accordingly, so it's easy to tell them apart.
8 - Power off, disconnect the old hard drive, boot again using the Ubuntu Live CD
9 - Follow these instructions to reinstall grub and make Ubuntu boot again
10 - Done! :-)
A few remarks, taken from comments so they don't look like a chat window:
If instead of keeping the same install you want to change from 32 to 64 bits, within the same Ubuntu release, you may simply install the 64 Ubuntu on top of the 32 (just select the same partition), and the install will keep your /home, settings and packages. And you don't even need to backup: you already have your old drive as one ;)
If upgrading version, I would consider formatting the partition and forget about restoring settings and apps. Because settings from an older app may not apply to a newer version of the same app. Even software selection is fuzzy: some packages are deprecated / renamed / not necessary in newer releases, so not worth the trouble. Just open Software Center and manually install the apps you want.
In this case, it really pays off to keep your "OS-independent" data files (Music, Videos, Documents, etc) in a separate partition, so "your stuff" is always available regardless of Windows or Ubuntu version installed.