How do I replace Windows with Ubuntu, yet keep my data?

Since the process involves a lot of steps, I think it'd be better to provide a link.

So here you have it: How to Install Ubuntu 12.04 Precise Pangolin

If you've any other queries, don't hesitate to ask.

If you want to retain any data which is stored in C: drive, make a backup either on some other partition or on some external media.

If you install Ubuntu in the C: Drive (where the windows is installed) everything in the C: will be deleted. (C: contains all the contents of your Desktop, My Documents, Recycle Bin, and in most cases all your installed programs and files related to them).

On the other hand, if you choose any other partition, the contents of that partition would be deleted.

Since you want to remove Windows and install only Ubuntu, you'll have to choose C: while installing Ubuntu. There will be a window like below while installation and there'll be plenty of other options in your case and I guess you'll be able to choose to remove Windows and install Ubuntu.

If not, you'll have to manually select the partition containing Windows and install Ubuntu on it.