There should be directions on the grout container.

I had a similar problem and tried vinegar with absolutely no results. I eventually resorted to using sulfamic acid and it worked really well and did not damage my glass tiles. I would highly suggest testing it on a small area first to make sure it doesn't damage anything. If you do go that route have adequate ventilation going and protective clothing especially gloves and goggles.

I managed to clean some haze by using just microfiber cloth and water. However it takes lots of time and elbow grease, and it is very hard to clean the edge/corner.

I noticed that if I wipe across the grout line then sometimes the grout will dissolve and drip to the the tile below it. Should I wait for a few days before cleaning again? Or by that time the haze would be too hard to remove?

Also, does vinegar and the aforementioned acid consider abrasive? The tile instruction said I should use non abrasive cleaner.

If you paid to have this done, I'd be calling the tile guy, that's his job.

I just happened to come across this post tonight and I think I can actually contribute something! I've worked for 25+ years in the stained glass hobby and the best thing I've found to clean the haze is rubbing alcohol. Just pour some on a clean T-shirt material rag and rub off the haze from the tile. It should not take a lot of effort and I doubt it would harm the grout, but test a small spot first. Use a second clean tshirt to polish it to a shine. Hope this helps!

There are two separate cleaning projects here: the fresh buff with recently applied grout, and maintenance cleaning. Haze doesn't get harder as it ages because haze is portland cement that's hyper thin and un-set, only dried.

Freshly, the simplest approach is buff with a dry cloth. Vinegar will cut the haze but it will also leach from the grout a little, particularly if it's fresh, so vinegar is not appropriate at this stage. It's like rubbing off the old haze and reapplying fresh haze right behind.

Glass will scratch, hence the non-abrasive cleaner for maintenance. If you're using chemicals that are so hazardous that you need extraordinary protection from them, some rethinking may be needed.