Do not dress over the top but also do not dress like you were in the middle of a paint job and decided to drop by. A bit of formal dressing will be enough and will reflect well upon your personality. A jacket and dress pants would be great and you will look classy wearing them.
Make an entry like you will come to any event and do not make a loud appearance. It is against manners in any place and certainly not acceptable in an art gallery. Once you come, there is no problem in talking or chit chatting but be sure that you are not very loud. Doing so is likely going to get you the disapproval of many fellow art lovers.
Do Not Touch Art Work
Make sure that while you enjoy the art work and have a good look at it, do not touch it. Some people can be extremely edgy if someone touches their work and the situation can get heated up pretty quickly. So enjoy the art work, just do not come in contact with it.
Talk About Art
If you are talking to someone, particularly someone you have just met or know very little, it is best to focus on the art work and forget the rising prices of the fossil fuels or how annoying your boss is. Also do not talk too critically about the art work or the artist and its best not to compare it with the art work of others.