Before trying to install Linux, get a full inventory of what your computer has. You might have to help the installer recognize the hardware. Also make sure that your hardware manufacturer supports the Linux distribution of your choice.
There are many ways to install Linux (from a CD-ROM, FTP, HTTP, NFS, a DOS partition, etc). If you are a beginner or lazy (as I am), do the installation from a CD-ROM. Just put the disk in the CD-ROM drive, wait and boot. Do NOT forget that the installation will format the partition where you install the OS. If you want to test Linux without doing any changes or formating your HDD, get a copy of any live disk, which has become common practice nowadays.
A simple way to install Linux is to create two main disk partitions, a /swap and a system native. As a rule of thumb, make the /swap partition (virtual memory, written to disk) twice the RAM that your PC has. For example if the PC has 256 MB of RAM, assign 512 MB for /swap. Allocate the remainder of the HDD for the /root partition and make sure it is primary and bootable. You can also create a partition for user accounts (/home) and another for user installations (/usr). Neither of the latter two partitions are destroyed when upgrading the OS. To create the partitions, refer to the manual included with the system that you are installing. A good technical reference is the downloadable Slackware Book even if Slackware is not your Linux distribution of choice.
Then again, if you want to install Linux easily and painlessly with mere questions to configure the system, you can try Ubuntu based on Debian. I have been running Ubuntu for several years already without any complaints, other than installing the codecs to play DVDs manually.