I send thank you 'emails'
After I thank them for their visit and tell them how much I enjoyed meeting them, I tell them that the best form of advertising comes from my guests and include a link to the Inn on TA. It reads something like this:
It is free and easy to register on TA, only a couple minutes. Make sure you let others know what you liked/didn't like in the area or the Inn. If there were any problems with your stay that went unaddressed, please don't hesitate to let me know. Future guests will thank you!
I send a thank you email. I would never ask for a 'good' review, but I do give the guests a link to a review site in case they are of a mind. 99% of the guests are not of a mind. (The review site I link to changes as my whimsy takes me.)
I always emailed a "thank you" message to my guests. At the end I said something like " if you would enjoyed your stay with us and would like to submit a review, click this link. And then had the link to our "review" page.
That always worked for me.
Always a thank you email (it was part of my reservation system and could be tailored to the guest). I would link to our review sites in the email.
Memorable guests or guests that had done something special FOR US, got a handwritten thank you note. Sometimes, I'd include a business card with a discount for a return visit.