If you have a single telephone line and it's a simple voice line, which is the basic sort in the uS, when your computer is connected, anyone calling you will get a busy signal, since the line is in use.
If you have "call-waiting" the incoming second call will try to tell the "person who's talking" that there's another call. Since the "person who's taliking" is your computer, this will often break your web connection, but won't necessarily ring the phone.
Since this kind of telephone line can only handle one call/one connection at a time, I haven't heard of a mux that would do you any good. If you get enough calls while you're on the web to interfere with web use, your modem can be set up to include the code to turn off call-waiting when it dials the number for your web connection.
If you're in an area (of the US) where voice line is all you can get, usually the only way to be able to talk and surf at the same time is to have two separate lines.
If you can get a more sophisticated connection, such as a DSL line, where the line can carry two separate communications at the same time, the hardware supplied with the service should take care of separating voice and web. You usually have to install a filter, often on each voice telephone, to prevent the higher frequency signal used for the web from being seen by your voice phones.
This is what's the common situation for US phone systems. There are significant differences in the kinds of services provided in other countries, so some systems may permit multiplexing of calls by the phone service user. There may even be rare US services that a mux-capable, but I haven't heard of any. If anyone has more information on where and how it can be done, it would be of interest here.