Be careful now, this question is a loaded one. Visiting is one thing, short term stay is another, long term / moving permanently is what I am talking about.
In a nutshell, moving to Germany from USA without anything is difficult. Meaning, no job, no language skills or connections of any kind. You would need to have a bit of money ready to support yourself, find a job fast (in less than 3 months). You also have to ask for an “allowment” to work in Germany on your resident permit that you would get from the government. This costs a bit of cash. Once you have this, you can then stay. Usually up to 3 years before a renewal is needed. Now, the “variables” regarding the right to stay in Germany from the USA are almost equal to the complexity of paying taxes in USA. You literally have to talk to the government for non-citizens to see what you have to do.
Now, if you are married to a German citizen then its less complicated, but there are still critical steps you must follow. Proof of marriage, Translation of the international version of your marriage certificate by a certified translation company.
If you have a skill that Germany needs….then in short, they roll out the red carpet for you. .