First

The most valuable advise I can give to dial up users is: switch. Get DSL or Cable or Satellite. With Windows XP and Vista the amount updates flowing to your computer for Windows, Office, Adobe, and your security software can literally swamp a dial up connection for days at a time. You turn off these updates at your peril. Switch.

Making the phone and internet work together

Internet Dial Up connections use an existing phone line. A problem that these users have is losing one connection to make the other. This page discusses four solutions to this problem. You can answer phone calls while still maintaining a dial-up Internet connection.

Method #1: a v.92 56k modem + Call Waiting
v.92 modems come with the option to place the Internet connection 'on hold', so that the user can take an incoming call. The Internet Service Provider must also offer the v.92 service and you need Call Waiting from your local phone company. Cost: $25 ~ 50 for a decent v.92 modem + Call Waiting. Shop for modem at Nextag or Price Grabber

Method #2: a Hardware Switch Board
These devices split the phone signal into three separate lines, computer, phone, and fax. There's no software needed and no installation. Calls cannot last more than 20-30 seconds. Call Waiting is required, from your local phone company. Cost: about $40 ~ $50.
The Emerson Switchboard or the The Catch A Call Switchboard

Method #3: Call Answering / Managing service offered by a local phone company The call is either answered by the telephone company's "answering machine" (Voice Mail) or forwarded (via Call Forward) to another phone, such as a Cell Phone. Cost: about $5 per month, depending on your local phone company.

Method #4: Internet-based Call Waiting Phone Alert Services.
Internet Call Waiting Phone Alert Services will display a Window and show that there is an incoming call. Features vary, depending on service provider. You are connected to the Internet via Dial-Up modem (phone).There is an incoming call. The Caller's identity is collected and forwarded to a central computer which is connected to the Internet.The central computer forwards Caller ID to you via the Internet, and alerts you of an incoming call. Depending on the service provider, a call can be answered, ignored, forwarded, or even sent a text-to-speech message on your behalf. All services require Call Forward On Busy from your local phone company. Cost may vary from around $.75 to $1.50 a month. Service Providers:
First there is Call Wave Then there is BuzzMe/RingCentral

Or you could just spring for that second phone line.