Public opinion is how people think of current issues as well as of the Liberal Crime Squad. To get a description of the current public opinion, one of your Liberals should be set to search opinion polls (available in the Liberal Activism menu). The accuracy of the results given depends on the Liberal's Computers skill, so it's best to leave the task to a Programmer or someone with a high Computers skill.
Public opinion is very important. The status of the current president is by far the most important part of the public opinion. The chances of the president staying in office can be seen as the approval rating at the top of the opinion polls screen.
The most important current issue can be seen just below the presidential approval rating. Below that there are two pages of current issues displayed in colors matching the public's view of them. Red is for Conservative and green is for Liberal, as usual. If the screen first appears as a big red mass, don't worry. The attention of the public is easy to get. The easiest ways to influence public opinion is to infiltrate according locations. For example, if the public doesn't oppose nuclear power, you should send a squad to a Nuclear Power Plant. Every location in the game has a few issues associated with them; successfully infiltrating these locations will make the public opinion on these issues more Liberal.
The most important current issue to the LCS is the Conservative Crime Squad. It is EXTREMELY important that you make sure the public respects the LCS more than the CCS, otherwise the CCS will catch the public eye and you will be forgotten. As you kill hundreds of conservatives the public will begin to respect the LCS and hate the CCS.
The closer to Elite Liberal the public opinion is, the more Liberal (and Elite Liberal) congressmen are likely to be elected, and the more are chances that the next President / Vice President will be a Liberal (or Elite Liberal). The public opinion also influences how much of the population seen on the locations is Liberal.
The second best way to catch the public eye is to run special editions of the Liberal Guardian. If you have obtained documents pertaining to a certain issue, publishing them in a special edition will improve the public opinion on them significantly. This may also be risky, as some of the documents (like the CIA files) will attract raids, and is illegal if the Free Speech laws are Arch-Conservative.