As photographers we are rarely encouraged to take pictures of someones else's photographs when they are exhibited. It is considered naff in some cases and criminal in others - particularly if we then whack them on our websites and claim them as our own.
It's a little different if we go to see pictures that have been done by other means - or sculptures or artefacts and manufactured articles. Sure, there can still be a degree of taboo, but many public galleries are okay with it - as long as you do not use flash or tripods.
This is fine - I love wandering the art galleries of Victoria and New South Wales to see famous works of art - and new, obscure things. I have learned to cope with the light conditions of the places and to get a clear result.
The illumination can be problematical, though good galleries will have directed lighting that shows the art to good advantage. But the colour temperature of it may be all over the shop. I've taken to recording the art with RAW and a small jpeg - the little one as a sighting rifle for he more detailed capture. I have also considered one of the tiny Spyder Checkr 24 colour cards for my travelling bag so that I can reference back to a neutral result later on my computer.
Flash is out - the galleries do not want to subject the works of art to the danger of fading or the cleaning staff to the danger of discovery...put your camera up to the highest ISO that will deliver a clean image for your purposes, and turn the image stabilisation on. Consider attaching a Steadepod to the bottom of the camera and stepping on the footplate whenever you need utmost stability.
Lens choice? Well, if you have a lens that has very little distortion in the first place - like the 23mm f:2 on my Fujifilm X 100 - you need not worry. If you are using a zoom, do a little investigation beforehand to find out the focal length that will have the least barrel or pincushion to it - somewhere in the middle of the range.
Stop it down one stop from wide open if the lighting permits. Nearly every lens gains something from this.
Try to stand square to a flat work of art, or at the most attractive angle to a 3-D object. If the thing is big and you are standing on the floor you are likely be tilted up and getting some keystoning - correct it later with DxO or Photoshop. If you find that you can capture the image you want from further away in the gallery wit a longer focal length the keystoning will be less evident.
Be prepared to experiment. Circular polarisers can sometimes help with the view through a glass cover - sometimes not. Painters who have decided to express the grace and beauty of life with a trowel and mortar board are likely to have left a problem, as the surfaces of their works reflect light everywhere. You are allowed to curse them quietly.
You are also allowed to quietly abominate the crowds of people who will surge in front of you just as you press the shutter button. Patience - they will drift onwards eventually and if you wait you will get a clear shot. It is the same at a car show - the gawkers and strollers sometimes work in tag teams but eventually they tire.
Final note. When you bring someone else's vision home to look at you are free to look and free to admire but you are not free to publish it out. There are still laws for this. The artist might be dead but you can bet their lawyers are alive.