John all you need to do is install the blog somewhere on your site, typically in a subfolder of the main root folder. Chances are your root folder is called either public_html or htdocs. (It can be called something else, but those two are very common) You might then create a subfolder called 'blog' and install the blog software in the new 'blog' folder.
The blog software you decide to use will usually come with some instructions for how to install it. I used WordPress for my blog and the installation was very easy. You download everything at the
Wordpress site. The files will all be zipped so you'll need a program that can unzip them.
Within your hosting account you'll need to set up a database and instructions to do that should be provided by your webhost. It's usually a matter of clicking a few buttons, and creating a username and password to access the database.
In the WordPress files there will be a config.php file which you need to edit slighty. You basically need to provide the username and password you just created for the database as well as a hostname. The hostname can vary depending on your account, but often it will be 'localhost.' You will need to find that information from your host.
Once you've edited the file you upload all of the WordPress files to your 'blog' folder and using a broswer navigate to yourdomain.com/blog/wp-admin/install.php. That file will attempt to access your database and create a username and password to access the admin side of your blog. Assuming all went well you can then login to your blog and start posting.
There are other things you may want to do with the blog like customize the look and their are different ways to set things up, but the first step is installing the blog software. I don't know from experience the install procedure for other blogs, but I would imagine it's pretty similar. It really isn't too hard and I promise you many people here will be happy to help if you have any problems.
When you want to link to the blog from another part of your site you would use yourdomain.com/blog/ or possibly even just /blog/
It really is pretty easy. Start by looking at different blog software and deciding which you want to use. I think WordPress is very easy to install and use and maybe be a good one to try since this is new to you.
If you have more questions don't hesitate to ask.
