Hi Lynn71,
Generally speaking, expats can adopt while living here. You have to have a home study done in the canton where you live. Many expats choose to adopt from either the USA or from agencies that are based in the USA. Instead of going into great detail here, check out this website:
http://groups.yahoo.com/group/adoptsupportswitzerland/
It should have answers to many of your questions and yet leave you with a million more. Good luck!