You should be able to install Linux on your machine, one question is whether you want to wipe out what you have or not.
I am not sure if the current version of Fedora Core has the ability to resize a windoze partition or not. Knoppix has a program, qtparted, which can resize a partition, but you should backup and defragment the disk first.
To install it, boot the CD and follow the prompts. You need to decide how you want to partition the disk and there are many choices. Personally I recommend a 100Mb /boot partition, 4Gb or so root partition, 512Mb-1Gb swap partition, 4-10Gb /home partition and then the rest is more of an option, such as a secondary root partition so that you can install an upgrade and test it and the other data partitions.