Well the typical anonymous surfing site, will have a page usually with lots of adverts with a place to enter a URL and a GO button. When you type a web address into this section then the web proxy will go off and deliver it back to you. Now the experience varies with many of these proxies from this point - some deliver your page in a frame (with adverts around), some just deliver you a page with some ads at the top and a url to return or type another web site.
There are lots of advantages to using these anonymous surfing sites, obviously the fact that they are free is a big bonus, you don't need any technical skill or to change any of your browser settings. The main advantage to anonymous surfing is that when you visit a web site it will record the IP address of the proxy and not yours.
Don't worry too much about the adverts, they can be annoying but at least it shows a legitimate way of financing the running of the server unlike the 'free anonymous proxies' list which contain a very large proportion of servers which contain viruses and loggers ready to steal your passwords and accounts.
So what are the Drawbacks of anonymous surfing sites?
The most important point to remember is they don't really offer complete anonymity - they only hide your IP address from the server you are visiting. That's it if anyone checks with your ISP there will still be a full log of every web site you have visited, the web proxy you use will have a log of which web site you visit and your browsing will still be in clear text so will be accessible from lots of other points.
They can be slow for any complicated sites, many have problems with SSL (secure sites with a padlock at bottom) and of course don't expect to be able to view any multimedia type content.
I would say they are ok for occasional use as long as you don't expect any real anonymity, using them to access a forum where your IP is banned might be a good use.
I won't recommend any as there are too many hacked and virus ridden servers and I do't wish to accidentally point someone at one of these ! Most of the web based anonymous surfing sites seem to be ok though - use at your own risk though.
If you want real anonymity on the internet you need to use a real anonymous proxy to hide your IP address and location, and protect your browsing via an encrypted tunnel. There are a very small number of systems that do this but the best in my view is called Identity Cloaker - its is a small portable application which you can even run from a USB stick for use at work or college.
It will encrypt your entire connection unlike the anonymous surfing sites, blast through firewalls and content blocking proxies, then allow you to surf via a fast private, and secure proxy server from the large selection in different countries. It is is a different league from anonymous surfing sites and offers true anonymity combined with fast, secure surfing.