There are many web hosts in the world that offer Wordpress services. When you go to pick one make sure it meets the minimum requirements set by Wordpress. I have been a webmaster for the last 7 years and I use BlueHost and have had nothing but a positive experience. Wordpress also recommends using BlueHost (Click Here)
The best part of the BlueHost product is the easy install and automatic updates. The hosting package is also as great deal, you get:
To sign up visit www.BlueHost.com and sign up for a new account. The cost should be around $100 for a year of hosting and domain name.
Once you are signed in go the c-panel screen. It should launch automaticallyIf you still don't get it check out the how to install Wordpress video on the BlueHost support page
Now you have Wordpress installed, it is that easy. Next try signing in and learning about Pages and Posts. After that start looking for a theme to use.
In full disclosure I am a BlueHost affiliate but I really do love the product. I have over 50 websites hosted with them.