Enotes policy allows me to answer one question per post. I will answer the first question you posted.

Since you haven’t mentioned a specific war, I will focus on World War I. The government did several things to ensure that people were supportive of the war effort, including a few that were controversial. The government created the War Industries Board to coordinate the production of war materials. The government didn’t want businesses arguing over what would be produced, who would produce it, and how much would be produced.

The government also encouraged people to conserve food. People were encouraged to grow their own food in what was known as the victory garden. People were encouraged to not eat bread on Mondays and meat on Tuesdays. This was known as Wheatless Mondays and Meatless Tuesdays.

The government created the Committee on Public Information to sway public opinion in favor of the war. Posters, pamphlets, and speeches were used to accomplish this. The government also encouraged people to buy war bonds, which were often called victory bonds.

The National War Labor Board was created to help prevent strikes. Companies were pressured to settle disputes with workers in return for a promise that workers wouldn’t go on strike.

The government passed a few laws that infringed on people’s freedoms. The Espionage Act made anti-war activities illegal. For example, people who interfered with the draft could be jailed and/or fined. The Sedition Act made public opposition to the war illegal. People could be jailed for saying false things about our war effort.

The government did many things to ensure that people supported the war effort in World War I.

What were the methods used by the government to ensure public support for World War I?  

The major method used by the government to ensure public support of the war was propaganda.  The US government set up a major propaganda apparatus whose job was to get people to support the war both through their opinions and by loaning money to the government.

The main part of the propaganda apparatus was a committe called the Committe on Public Information (CPI).  The CPI produced many kinds of propaganda.  These forms included posters with patriotic and anti-German messages.  They also included the mobilization of a huge group of speakers trained to deliver propaganda messages to public groups.  Other tactics included the creation of pamphlets and movies.

This sort of propaganda was the main way in which the government tried to win support for the war (as opposed to suppressing dissent).

Which were the methods used by the US government to ensure public support for the World War I?

One of the primary means of ensuring public support was the formation of a Committee on Public Information eight days after the formal declaration of war. Journalists, photographers, and artists were encouraged to spread information about the war in a positive mode. The committee promoted saving food and fuel and the sale of war bonds to support the war effort. The committee promoted the idea that anything German was tantamount to disloyalty to the American cause. For that reason, German Measles were called "liberty measles," dachhunds became "liberty pups," and that most German of dishes, sauerkraut became "liberty cabbage."

Additionally, the Espionage Act of 1917 and the Sedition Act of 1918 provided severe punishment for attempting to interfere with the war effort or distributing literature or materials abusive about the U.S. Government or its armed forces. Also, the Lever Food and Control Act created a U.S. Food Administration which encouraged Americans to observe meatless Tuesdays; wheatless Wednesdays, and porkless Saturdays, all in an effort to garner support for the war. Finally, Americans were encouraged to plant "victory gardens" to save food and promote the effort.