Most of the time, your computer come with a paid Windows. If you are not an experienced Linux User, it's probably better to keep this Windows, just for safety in case you have to show your computer to the vendor tech (If your vendor is Linux fiendly you are lucky!). So you have to make room for your prefered Linux.
If You have Windows XP, little luck. Most XP computers come with only one partition on the disk and XP don't know how to make it smaller (If you have two, see the next paragraph). What you have to do is to "defragment" the drive (look in disk properties, you will probably have to "verify" the drive first) - if the computer is brand new and never used, this is not necessary. The "defragmentation" makes the work easier for the Linux partitionner.
If you have Windows Vista, go to Control center, Administration tools, Disk tools to see the actual disk partitionning. If you have luck, may be there is yet a "data" partition. If so, you have just to look where is this partition located and what it's size is. It will be used for Linux.
If not, clic right on the system disk partition rectangle, you will see a resize option. Use it. Keep some room for Vista (50Gb, for example) and OK, you have now several partitions on your drive.
If you see in this screen a small partition (usually around 9Gb), be specially cautious. This is the "system restore partition" that holds the Windows Vista (or XP) original system. Your computer manual should explain how to copy this to two DVD's. Do this before any use of your computer. Make notice of the size and place of this partition (it can be at the very beginning of the drive or at the very end), try to not erase it right now. Don't erase it during the computer insurance time.
You, as a dummy Linux user, have better use a very well known Linux Distribution. There are more than a hundred Linux distributions and I don't have used all of them, of course, so I can't be sure some of them couldn't erase your drive if ever you don't understand a question.
However I'm rather sure Ubuntu, openSUSE, Mandiva, Red Hat Fedora, new Debian can be reasonably safe for a beginner.
So launch the Linux install. Probably you will have to insert a Cd or DVD and run. May be you will install immediately or launch a live system (Linux working from memory, not from drive), then install froms there.
Anyway, you will have to answer some basic questions and at a moment you will be asked if you want to keep windows or erase it. Beleive me, keep it for now, it will be easy to remove later.
At this moment you will be presented a screen with a graphic of the proposed disk partitions. Scan it to verify the Windows partition is not touched - not formatted. It is probably labelled "NTFS" or "Windows". Verify also that the Windows system backup partition is not touched. It may not have any identified label. In some partitionner, the partition table may be called Disklabel.
You may have to give Linux the name or position of the Vista partition created on the previous step. If your Windows is XP, you will be proposed to shrink the Windows Partition this is good.
Then accept the partitionning sheme your distribution proposes. Do not try to be an expert. At install time, no good Linux Partition tool should erase a Windows system partition. If it does, write me, I will include a notice here.
Modern Linux distributions are perfectly able to resize a Windows partition to make room to Linux. Let some room to Windows, though, if you plan to use it.
So, in summary, trust your Linux install. Most install problems are user's problem, not Linux Distribution problems!!
Do not try "LVM" or "RAID" for your first install. To use these things, read the hole Partitions-and-mass-storage-HOWTO.