Here are the basic pieces of the puzzle
Sometimes just called "Domain". This is simply the address of your website on the web. This is important because people should be able to remember this address, and they should be able to easily spell this address. Think of it like a phone number. You can get a phone number, but it does not mean that you have a place for that number to ring. And if you do have place, that place may not have any people or furniture or anything It may be empty. You may find it easier to register your domain at the same place as your hosting. This will ensure that the domain and the hosting are already connected. If you have a domain somewhere else, don't worry. It is not hard to tell the domain name what new server it should point to.
Domain names are usually renewed each year for between $10-$20
Web Hosting Server
Sometimes just called "Hosting". This is where the domain name sends the users who enter your domain name. Where do they go? They are directed to a computer (or really space on a computer) where the files that make up your website all live. Think of it like that office I mentioned above. Your domain name is like a phone number, the hosting server is like the office it "rings" to. Please note that unless you have put some files on your web hosting server, it will be like an empty office. The phone will ring but no one will answer. The job of your website is to answer the "ring" of your domain. Web designers and developers will put the files on your web hosting server that are needed to deliver your text, pictures, and other content when visitors "ring" or to use a more correct term "ping" your website.
Web Hosting is usually paid for in1 year or 2 year terms, and will cost be between $9-$18 per month.
As mentioned above in the "Hosting" section. Website design and development is the building of the files, and programming, or at the very least the installation of files on the web server, that create the actual website. These files cannot practically be be accessed on a local computer such as the one on your desk. They need to be installed on the web hosting server. How do they get there? Files are often sent over the internet using a special protocol called FTP or "File Transfer Protocol". Your web designer will usually need to have access to your hosting account to set up this file transfer account.
Smoke with a side of Mirrors - Who do you go to for a domain? How about Hosting?
This is a great question, but it has few clear answers. The good news is it is easy to do web searches to try to determine who has the best reputation. The bad news is that in almost 100% of cases, the information you will find has either been put there by a hosting company to improve their reputation or by another to blast the competition. In other words as you see countless pages of web hosting "reviews" and 10 best / 10 worst lists, know that they re all created to look "real" but basically none of them are really unbiased reviews. Also, I have seen many, what I consider"good" hosting companies, with many horrible reviews, and vice versa.
At the end of the day, web hosting companies, are like any other service provider. Think of phone companies or cable companies. Each has strengths and weaknesses. Some are cheap, some are fast, some have great customer support, some are technically superior in some geeks eyes, but at the end of the day you still need to decide.
To make the best decision, look for some basic things:
Cpanel Access - This means no funny proprietary dashboards you or you r web designer will have to figure out, as is the case with Yahoo small business and Godaddy (...Yes that's a hint)
Emails - Don't be fooled into thinking email accounts should be some additional charge. You should expect some email accounts with a web hosting account. How many? That will usually vary between 10 and 100.
Databases - SQL databases are needed to run Wordpress, Drupal, Joomla, ZenCart, and other CMS (Content management Systems) and Shopping carts. Most installations only need 1 database, but if you have a second website or installation of one of there above you may need more. Typically you should be offered 10-20 databases.
Multiple Sites - If you ever will have a second or third website, it is nice to know that you can just add another domain to point to your hosting server, and you don't have to pay to upgrade or worse yet, move everything to a decent web host that does allow more than 1 site per hosting package.
Operating System - Windows or Linux are the usual choices. Unlike your desktop computer, Linux is the more commonly used and most widely compatible server operating system. Windows will often work fine too, but for most general websites (and without getting into a bunch of tech stuff) choose Linux if offered the option.
The Temptation to buy cheap hosting is....well...Darn Tempting!
Trust me when I say that for every $3/month hosting deal you find there are several other $2/month options. Also, some $1/month deals, and for those of you who really love saving money, there are even some FREE hosting providers.
Whats the down side? Reliability is one. Server down time can be high on cheap hosts. Security is another important one. Reliable hosting companies watch their server environments to ensure no security loopholes are open, and that users are not running scam sites and other shady activities.