unless you two marry (or intend to do so in Switzerland), it's going to be difficult for you to get a visa other than a tourist visa.
You will get a work visa only if you have a contract by an employer. For non-EU citizens, this is fairly difficult to get unless you are a highly specialized professional, artist, scientist, or journalist (I assume you're not a US government employee, that is a different story again).
There are quotas for the number of admissions per year of persons from non-EU countries.
If your employer wants to transfer you to Switzerland, then that's definitely the way to go. Your employer will know how to do this, and you will also have to apply via the appropriate Swiss consulate.
Some information can be found on the site of the Swiss Foreign Affairs Ministry: www.eda.admin.ch/eda/en/home/reps/nameri/vusa/ref_visinf/visusa.html#ContentPar_0010
Hope this helps, and good luck!