This is a pretty big question, and the answer is, somewhat obviously, that it varied according to the country, and their relations with Germany at that moment in time.

In the United Kingdom, public opinion of Germany had been slowly cooling ever since Kaiser Wilhelm had denounced them as 'mad, mad, mad as March hares' in an interview in the Daily Telegraph in 1908. While Wilhelm was trying to say that he wished to improve Anglo-German relations, his remarks had the opposite effect. Germany's attempts to build up a fleet capable of challenging the Royal Navy, and their efforts to establish a colonial empire were viewed as directly threatening to British interests. While the German population of the United Kingdom was not as large as the one in America, standing around 53,000, they still formed a significant group. It's estimated that 10% of waiters and staff in London restaurants were German. Three major German banks, including Deutsche Bank, had opened branches in London and German firms and factories offered a number of services.

When war broke out, anti-German hysteria broke out on a large scale. There were anti-German riots which destroyed many German owned shops and businesses. The royal family were forced to change their name from Saxe-Coburg Gotha to Windsor, and even German Shepherd dogs were renamed to Alsatians. After the sinking of the Lusitania, anti-German riots caused £200,000 of damage in London and £40,000 in Liverpool. The attacks on German bakers were so severe that the capital experienced a shortage of bread for several days afterwards. In Australia, a number of towns with German names were renamed to patriotic sounding places such as "Verdun".

Germans also faced a number of legal restrictions. Germans were required to register with the Police, and restricted from working in certain jobs such as banking, although many existing bank workers were allowed to continue working under supervision. Additionally, patents granted to German firms or nationals could be suspended if an interested party made an application to manufacture something under patent. A number of German language newspaper were closed.

The policy on the internment of civilians developed very slowly. Initially, the decision was made to intern all German and Austro-Hungarian men of fighting age, but the Home Office eventually decided that only those who posed an immediate threat should be interned. This essentially meant anyone suspected of espionage, and any German citizens who were in the army reserves, several hundred of whom were arrested on their way back to Germany. Apart from these men, the internments were halted until after the sinking of the Lusitania, at which point it was decided to intern all adult males, although partly for their own safety. By November 1918 24,522 Germans had been interned, although this figure also includes the crews of captured merchant ships and fisherman who were captured in the North Sea. The Dominions also established their own camps, although the crews of ships interned in the Dominions at the start of the war were transported to Britain. After the end of the war, the Germans were gradually released from the camps either to return to their families or to Germany. Many chose to return to their homeland, especially since German owned businesses in the UK were confiscated as part of the reparations payments in the Treaty of Versailles. By the end of 1919, the German population in Britain had halved.

During the Second World War, the situation regarding German born residents in Britain was somewhat complicated by the fact that many were either political refugees or German Jews who had fled Germany before the outbreak of the war. Nonetheless, 74,000 Germans, mostly men of military age, were interned until it could be established that they did not pose a threat to national security. The vast majority of these men were released, and only around 2000 remained in custody. In contrast to the First World War, the public made a distinction between Germans and Nazis and so there were far fewer attacks on German businesses and citizens.

A similar situation took place in the US, although the vastly larger population of German immigrants and those of German ancestry made the practical application of internment somewhat more difficult. In both wars, only those deemed to be threats to national security were interned, although in both cases the Government pre-emptively interned Germans before they had entered the war. During the First World War, only 2000 Germans were interned, although this rose to 11,500 in the Second, a far cry from the hundreds of thousands of Japanese Americans who were interned. Since the US didn't have quite the same rivalry with Germany as the UK, anti-German sentiment was more limited, although there were sporadic bouts of anti-German violence and at least one lynching.

Hope this helped!

Sources:

Panikos Panayi, Prisoners of Britain: German civilian and combatant interneesduring the First World War, (2012).

Panikos Panayi, 'Anti-German Riots in London during the First World War', German History, Volume 7, Issue 2, April 1989, pp. 184–203.

Arnold Krammer, Undue Process: The Untold Story of America's German Alien Internees (1997).