First of all, we have to understand that “conservatives” and “liberals” did not all believe the same things about the US invasion of Iraq. For example, when they were senators, Barack Obama and Hillary Clinton did not vote the same way on this invasion even though we say they are both liberal. Therefore, when we talk about what liberals and conservatives believed, we are generalizing.
In general, both liberals and conservatives agreed that Iraq had weapons of mass destruction (WMD). Both sides believed that the Hussein regime had developed WMD and that it had not destroyed them. Though we now know there were no WMD in Iraq, both sides thought there were at the time.
In general, both sides thought that Iraq would be better off without Saddam Hussein. Both sides believed that Hussein was a brutal dictator who repressed his people savagely. Liberals and conservatives both felt that Iraq would be better off without him.
Finally, both sides agreed that it would be better for Iraq to be a democracy. Both liberals and conservatives believed that democracy is the best form of government.
The two sides disagreed strongly as to whether invading Iraq was the best way to solve the problems alluded to above. Conservatives believed that Hussein was likely to use WMD against America or its allies if we did not invade. They felt invasion was the best way to oust Hussein and make Iraq democratic. Liberals generally disagreed. They felt that Hussein was unlikely to attack us and that diplomatic and economic pressure could eventually make him give up his WMD. They felt that invading Iraq could not really turn the country into a democracy.
In addition, liberals were less likely to believe that invading Iraq was worth the benefits, particularly if we did so without UN approval. They felt that Hussein was not so bad that it would be worth it to the US to remove him. They felt that the international community would disapprove of US if we invaded unilaterally, thus hurting out ability to influence other countries.
There are other similarities and differences between liberal and conservative thought at the time of the invasion, but these are the most important.