Check with your hosting company. They normally install it for you or can tell you how to install it using an interface they probably provide to make it easier. Just make sure that the blog address is yourwebsite.com/blog, not on wordpress as yourblogname.wordpress.com, otherwise your site doesn't get the benefit. Make sure you tell them that if they install it for you.
It can be a bit tricky if you havent done it before, but if you get to that stage and you need more advice just message me and I can give you some tips. The easiest way to 'design' your blog (as the basic format for Wordpress is a bit dull), is to hire a cheap designer to make it look like the rest of your site, or upload a premade theme. Woothemes (www.woothemes.com) has some free ones that you could use. All you do is download the theme and then upload it into your wordpress admin panel. Again just let me know if you need some tips there.
Hope that gives you a starting point!
Having just gone around having wordpress installed by hosting company of a client...it was a nightmare. I wish I could have just done it myself. It took days to get it right. With my hosting company it is as easy as a click of the mouse to install. Then of course, you need a bunch of plug ins if you really want to run it right. But yes, you can do it, just create a sub directory called blog on your server and load wordpress there. then they url will be in your domain.
Wordpress has lots of FREE themes, if you alter any theme, create a child theme of your own because if the theme is updated, you lose. I had to start over on one because I never knew about CHILD themes before I started. Alot to learn.
I just did a woo theme site. I never saw any freebies on their site. We had to pay for it.
Lots of times the one-click installs by the host have issues. They are often out of date installs and update on their time schedule not yours.
Doing it yourself takes a little more work but if you can follow a few step by step directions, it really isn't too bad.
Misconception #1 Bigger sites rank better. It is not so much that bigger sites rank better, it is mainly that they typically have more traffic because they essentially have more hooks in the water. IFF well structured and huge, it is possible to have them rank higher for a given search. There are some cases where a blog can help establish a site as an authority which will help a site rank higher for some searches, but it is not as easy as simply starting a blog. There are also cases where starting a blog contibutes negatively and does more harm than good.
Misconception #2 A blog with an offsite domain gets no benefit. There is some benefit in branding the two together for credibility and recognition. There is some minor benefit to having a growth in internal content, however, there is another benefit from having incoming links from an external domain. There is no blanket "one approach reaps all the rewards" when it comes to this. There are pros and cons to be considered, that just following a one method is best recommendation wipes out unecessarily.