How do I brew an alcohol-free beer?

This question just came to my mind. Should I just force carbonation to the wort and voilá?
Or maybe I should ferment the beer regularly and then boil off the alcohol by keeping the beer at, say, 150ºF?

Do you have any experience on that?

Why would you want to?

Seriously though, I think the answer is no. Though I don't see why you couldn't aim for a low alcohol brew in the 3% range. Less than that and I would think you would have problems with fermentation.  I make session ales and light lagers with low alcohol from time to time. I make sure to add plenty of caramel/carapils to give it some body and flavor. You have to be careful though, since with that little flavor it's really easy to make an imbalanced beer.

Commercially, alcohol free beers are usually made through reverse osmosis. Another method is very low temperature freeze distillation. Both strip flavor along with alcohol.  With freeze distillation, you can probably heat the extracted sugar solution to 180oF for 30 minutes to blow off most of the alcohol, then add the sugar back to the thawed beer.

I tried heating whole beer to make non alc, with highly variable results a very long time ago. The main issues were oxidation and bacterial instability.

The main thing is that alcohol is part of the flavor profile of alcoholic beverages. Without it, the product almost always tastes lackluster.

I suggest looking into low alcohol beverages like Kombucha or Ginger Beer Plant where you get a lot of satisfying flavor for 0.5% abv.

I have not done this, so I don't know how it would turn out but this is what I have read and heard about making "very low to no" alcohol beers.

Design a recipe for a low alcohol content (less than 2%).  Mash at 160F to 162F to create long chain dextrin sugars and very little fermentable maltose.  Ferment and transfer into glass bottles or mason jars.  Stick these in a pressure cooker and bring up to boil, allowing the steam generated to escape.  I am not sure how long to boil, but you can condense some of the steam and taste for alcohol content.

You will need to transfer back to a keg and force carbonate or add just enough sugar and just a bit of yeast for it to bottle carbonate. 

Alcohol-free, not very likely.  But is should be very low in content.  Ethyl alcohol forms an azeotrope (bound form) with water, so you will never get it all out this way.

The issue is always trying to maintain some beer-like body and flavor while driving out the alcohol and not leaving too many fermentable sugars behind, as these will make it too sweet.