The instructions here are based on this set of instructions (thanks to taternik, the author).

First, I made sure that the card works via Windows.  The preinstalled Windows has a Tool for configuring the Card.  Make sure that everything works there first.  I disabled PIN-entry.  Supposedly there is a way under Linux to have a pin-prompt, but I skipped that part.

Two new files have to be created as root:

/etc/ppp/peers/vodafone

###########################################
#Suggested Vodafone PPPD configuration file
#File /etc/ppp/peers/vodafone
###########################################
#Set this to the device allocated to the GlobeTrotter
/dev/ttyUSB0
#Baudrate
115200
#Idle time for closing connection
idle 7200
#Lock the device for this PPPD process use only
lock
#Use normal handshaking
crtscts
#Assume it is a modem device and force modem control methods
modem
#Any user can start the connection
noauth
#If a default route exists replace it with the ppp link
#You get an error if this command is not supported
#by your version of PPPD
replacedefaultroute
#Make the ppp link the default root
defaultroute
#Username and Password for computer/GlobeTrotter ppp link
#Normally ignored. Change if GSM Operator requires it
user vodafone
password vodafone
#Change the path to chat if required for your version of Linux
connect "/usr/sbin/chat -V -f /etc/ppp/peers/vodafone-chat"
#Accept IP address provided by network
noipdefault
#Detach PPPD from console used to run the program {optional}
#updetach
#Get DNS addresses from operator
usepeerdns
#Don't use VJ compression for ppp link
novj
###########################################
/etc/ppp/peers/vodafone-chat
# Suggested chat script called by PPPD
# File: /etc/ppp/rogers-chat
###########################################
ABORT BUSY
ABORT 'NO CARRIER'
ABORT ERROR
REPORT CONNECT
TIMEOUT 10
"" "AT&F"
OK "ATE1"
OK "AT+CGDCONT=1,\042IP\042,\042web.vodafone.de\042"
SAY "Calling Vodafone UMTSn"
TIMEOUT 60
OK "ATD*99***1#"
CONNECT c
###########################################
###########################################

Almost done! Now we only need a way to start the connection.  This must be done as root with the following command:

sudo pppd call vodafone

For convenience, I created a launcher with the type "Application in Terminal".  When done with the connection, it can simply be stopped with a Ctrl-C.