Can I install gapps after I have finished installing the new ROM? I have recently installed a new ROM on my Galaxy S3 and I did not flash gapps with the ROM itself. Can I go to reboot mode and flash gapps even after I installed the ROM?
You should be able to do that. First make sure you download the correct version (the version of the GApps archive must match the Android version installed on your device). Put the gapps*.zip file on your SDCard, and boot to recovery-mode. Select "Install update.zip", and navigate to your GApps archive. Select it, have it installed, reboot, enjoy :)

As you've tagged your question cyanogenmod, you might also wish to take a look at their GApps page. This will make it easier for you to find the correct GApps archive.