I had to figure out various PPP parameters (and associated Cisco IOS behavior) and didn't have real dial-up equipment in my lab setup. I could have gone with PPPoE, but it turned out it's way simpler to emulate dialup connections (at least the PPP negotiations work as expected) on fixed serial lines. This is the minimum setup you need on the “caller” side …

interface Serial1/0
 ip address negotiated
 encapsulation ppp
 ppp authentication pap optional
 ppp pap sent-username client password 0 client

… and this is the “server”-side configuration:

interface Serial1/0
 ip address 10.0.0.33 255.255.255.252
 encapsulation ppp
 peer default ip address 10.0.0.34
 ppp authentication pap callin
!
username client password client

To trigger PPP negotiations, shut down and re-enable the serial interface on either side.

Note: As I'm using PAP authentication, I could use the more secure username secret configuration command, which would not work with CHAP.