How do I install a vent-free fireplace?

Do you mean"vent free" fireplace?

Annie: Is this what you mean?

https://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Dgarden&field-keywords=table+top+fireplace&rh=n%3A1055398%2Ck%3Atable+top+fireplace

If so... I have three of them... and they work well.

Really think this thru. Unless They are really improved after using leaves a very strong burnt chemical smell. Plus if not set up correctly can be dangerous, I don't trust them. Everyone I know that got one either yard saled them after 1st year or left them but never turn them on. Go with vented and be safe. An honest sales person will tell you they wouldn't put it in their home.

You can buy a vent free, free standing fireplace.

Electric fireplaces. Can get stand alone too.