Shared hosting can be paid or free hosting and dedicated hosting alway requires a fee.
Before discussing the hosting types, it is important to understand the meaning of the terminologies bandwidth and storage.
Bandwidth is the quantity of data that your site can transfer in a particular period of time. This is also referred to as transfer. When your site is viewed on the internet, it is being downloaded from the server and this uses your bandwidth. Storage is the amount of hard drive space your site is allowed to occupy on a server.
Dedicated hosting is where your site gets one whole server to itself. You are basically entitled to all the resources offered by the server. The entire hard drive capacity and bandwidth is yours, including processing memory and whatever else. With large, traffic intensive sites, dedicated hosting is highly recommended. However, shared hosting is normally more than enough for individuals and small to medium businesses.
Shared hosting is when the hosting company puts your site on a server with sites from other customers. The hosting provider will normally give monthly limits for storage, email accounts, bandwidth and such. Depending on which server your site was put on and how effective the hosting provider is, at times things may get a bit crowded on the server and cause your website to be unresponsive and slow.
Free hosting refers to shared hosting which is offered by free hosting services. It is usually very limited. A times, you may 'earn' a good free hosting account by writing posts in forums. However, paid hosting and real domain names are much better.
Paid hosting is relatively inexpensive nowadays. You can get good reliable hosting that can support a small business for less than $100 per year. Normally, hosting providers offer free setup and a free domain name, as well as a money-back guarantee.
If you decide to pay for hosting, great caution is called for. You will not want to find yourself with the wrong web host. Read articles on choosing the right domain name and read reviews of web hosting providers. It is wise to go with companies that relatively big and established. Many people have lost their sites when new and unstable hosting companies collapsed.