Analytics of the website of the company I work indicate a 700K+ unique page views per day. I'm curious to know if there is any benefit from asking our visitors the NPS (Net Promoter Score) questions on landing to our website or after a task, page impressions, time on a page, etc.?
Well - the idea behind doing a NPS survey isn't to get the "best" score. It's to get the "correct" score.
One of the classic ways it's misused is to only ask it in contexts where you are likely to get a more positive outcome.
For example: If you sell a product that tends to break after a week of use you'll get very different NPS scores if you ask before purchase, just after purchase, or a month after purchase.
Likewise in a service industry people will likely forget the interaction if you wait until a few days/weeks afterwards to ask the question.
So really you want to be asking at the point where:
I'd also strongly consider looking at different cohorts when taking the test. If you group your new customers with your regulars you bias the results since - by definition - regular customers are going to be somewhat happy with your offering otherwise they wouldn't be regular customers.
I am a practitioner of the behavior model described by BJ Fogg at Stanford University. I can offer a theoretical answer based on applying behavior design .
In a nutshell, a behavior is most likely to be triggered when the actor has the ability to easily perform the action and is motivated to do so.
Motivation is difficult to increase. So the first thing to do is make the behavior easy to perform. (Increase the ability) So, no matter what, offer a sharing tool that makes it really easy to share the site. There are many pre-made sharing tools out there. I leave that up to you.
Different people have different levels of motivation. It sounds like you have analytics that might be able to identify users potentially more motivated to share... Return visitors for example. If you track users, put the share trigger in front of them when they are on the site.
Finally, motivation occurs in waves. If you can identify a time when a visitor is most likely to be in the mood to share, that is the time to introduce the trigger. I think at the end of an article for example is a good time to expose the share tool. I am thinking of the way news sites slide a link to the next article at the bottom of the page... well do that with the share tool instead.
In short. Make sharing really easy to do. Expose a trigger to share to motivated users at a time you think they are most likely to share.
All about behavior design http://www.behaviormodel.org/
If your company's site provides some product or service, then you can ask your user NPS questions once they have purchased that product/service from using your site. To make it less painful for the user, you can offer some discount or coupons for each reference made by the existing user. If the user is only using your free services, you can offer him paid services for free (or with some discount) for referring your site to their friends.