The State Archive of Lucerne (Switzerland) is a excellent source for this topic. I found valuable information on emigration which is always also a topic of immigration. Maybe specific for the Swiss emigration was the a large share of emigrants headed to foreign countries to be soldiers in foreign armies.
Example USA: Between 1815 and 1915, some 30 million Europeans arrived in the United States. For many it was a long and arduous journey. In the early part of the century, just getting to a port of embarkation might mean days or weeks of travel on foot, by rivercraft, or in horse-drawn vehicles. Because regularly scheduled departures were rare in the age of sail, immigrants often had to wait in port for days or weeks before their ship departed.
In Northern Europe, many immigrants departed from Dutch or German ports like Amsterdam and Bremen. Later, when immigration from Central and Eastern Europe was on the rise, immigrants often had to travel down the Danube River to Black Sea ports like Constanta and Varna. From there, they had to endure weeks or months at sea aboard sailing ships subject to the vagaries of wind and weather. By the way the Emigration Museum in Bremen, Germany is an excellent museum and I recommend to visit this institution when you there. I had much fun and it was quite educating.
The spread of the railroads across Europe in the mid-1800s greatly shortened travel time to embarkation ports, while the introduction of steamships cut passage time from weeks to days, in the case of the fastest ships. Ships also increased in size, some carrying more than 1,000 immigrants in steerage class.
Except in places where immigration was restricted—like the Russian Empire—it was fairly easy to travel from an obscure European village to the United States by the late 19th century. A potential immigrant contracted with a shipping company agent, often a local cleric or teacher, who informed the head office at the departure port. The agent then received a departure date and ticket voucher, which he passed along to the immigrant, who boarded a train for the port city. If the port of embarkation was Bremen, immigrants could almost step directly from the train onto their ship—the city had railroad track leading right onto the docks.
Between 1882 and 1917, the U.S. government introduced laws regulating immigration. In 1891, for example, Congress barred from admission those “suffering from a loathsome or a dangerous contagious disease” and those “convicted [of] a misdemeanor involving moral turpitude” like anarchists and polygamists. As a result, steamship lines became increasingly careful about whom they let on board. Immigrants had to have their papers checked and their health inspected before departure. Sometimes immigrants had to spend several days awaiting boarding, during which they were lodged and fed by the steamship company.