Some more information might be helpful. I was able to find a census of 1900 from the state of Conneticut that might contain your great grandfather with his wife and their 7 children including a Frank who later married a Jessie. If that sounds familiar to you then your great grandfather might have immigrated in 1887.
People crossed the Atlantic Ocean mostly by steam ship at that time. There were several companies that were offering to transport goods and passengers between various European ports in Germany, Netherlands, England, Italy and the United States. Most people arrived via New York, but there were a few other ports. Arrivals in New York are quite well documented and are also available online so if you are not able to find something there then the names might have been spelled differently by the ship or immigration officials or they might have arrived via a different port.
I found a "Josefe Kohl" which might or might not be your great grandfather who arrived in 1888 in Baltimore, Maryland.
If you want to know how travelling on a steam ship was then you might consult e.g. Wikipedia about steam ships or about the different shipping lines e.g. the Hamburg America Line. Generally it was like that that on such a steam ship there was a lot of freight on it and a lot of different passengers. There were only few cabins and much more "third class" rooms for several persons. I imagine it to be crowded but it could be also a bit luxurious if you were able to pay for it which most people weren't able to do.
Regarding the maiden name of your great grandmother I assume that you spell it how it sounds so the German writing of it might be "Vinzenzia Pucher". Did your great grandfather happen to work in mining or related jobs? I'm asking because there was an Austrian area with mining where the industry collapsed at the end of the 19th century which caused quite some people to emigrate to the US.