Your laptop should have one of the following:
HDMI - which can connect to HDMI or DVI (with an adpater) ports on the monitor
DVI - Which connects to DVi,or possibly HDMI or VGA/Dsub (with an appropriate adaptor)
VGA/Dsub - which connects to VGA/Dsub or possibly DVI (with an adapter)
DVi can be analog, digital, or both. A digital only dvi port would be unable to connect to an analog only DVI monitor. Fortunately most dvi is the 'Both' type these days.