As a computer technician I go through a very similar process everyday. The most common problem people have is downloading and installing what is called adware. This is the start of more serious infections but is in it self not extremely dangerous. Adware is mostly annoying, adding toolbars, pop-ups, and slowing your internet experience down. the most common side effect of adware is search redirections. This is where things can get worse very quickly. Lets say you go online and search for something, oh, lets say shoes. So you type in what you are looking for and instead of getting a Google or Bing search result you get 100's of search results that might look like they are legitimate websites only to find out that they are all sites containing more malware. So you go down the list looking for a site selling shoes only to get more and more malware the more you look.
Another source of problems is free downloads online. Everyone wants to get something free on the internet and, of course, there are a lot of good free things out there. However, you have to be very careful where you go, what you download, and when you install programs watch all those little check boxes during the installation. This is where the adware initially comes from 90% of the time. Below is a list of the most common adware programs that you should remove if you see them in your "programs" list.
The video below is a visual walkthrough of a very typical basic system cleanup using the Windows XP Operating System The process is the same for any computer, however the individual steps may vary slightly.