The Gapps zip file is in the same format as the CyanogenMod ROM, and as such needs to be installed in a similar way. However, unlike the ROM installation, Installing Gapps won't remove anything (other than currently installed Gapps, if any) from your phone.
You need to boot into your Recovery (Based on your previous question, this will be ClockWorkMod Recovery) and install that zip file in the same way you installed the ROM. Booting into recovery mode will be easier now that you have CM installed. I believe you should just be able to long-press the power button to get the reboot menu, and select "Recovery".
Edits may be helpful, but if I'm remembering CWM's process correctly, it'll be:
Install from zip
- (Find and select the gapps.zip file to install)
Also go to
Advanced and clear your cache and dalvik cache afterward.