How does remote server work?

I'm concerned that there will be a performance hit if there is a large 
amount of data transferred over a slow link.  Does the actual search 
occur on the client or the server side?  If on the client side, then how 
much data is transferred?  If it's on the server side then can I assume 
that a small amount of data is pushed to the server and just the results 
returned?

Thanks,
Jim.