I am trying to create giant museum display photos by using smaller photos. I'm clueless on cameras, so I don't know if what I'm asking is even possible, or if there's a much simpler way. Whenever I try to stretch the photos I have with photoshop, they become too pixalated and blurry. I'd like to print my display photo on a standard 8.5 x 11 page, and then take a high resolution photo of it so that when I stretch it to 6 times it's original size (51 x 66) it will look as good and sharp as the original small pic. What kind of camera or other equipment or knowledge would I need to accomplish this?
You can't stretch anything past it's size and have it be perfect, even in analog. It's like taking a gallon of water and trying to fit it in a 6 gallon bucket. You'll have 5 gallons of empty space unless you make each molecule of water 6 times it's normal size. Which is what your resizing is doing with the pixels, making them 6 times larger, so 6 times less sharp. To make the large image sharp you need to have an image with enough pixels to "fill your bucket" so to speak, without any extra space. So 6 gallons of pixels, to use the water analogy.
You need to take the original picture with a high-res camera.
For example, the earth photo NASA released in 8,000 x 8,000 pixels at 96 dpi is 83x83" in size. That is a 64 megapixel image. A good pro digital camera is around 20 megapixels.
To print out a sharp photo on 51" x 66" paper you will need to shoot at maybe 40-50 megapixels.
I suggest you take your requirements to a photo place and ask them. There are some others on the forums that I'm sure are way better at photography than me and may have some suggestions on here, but talking to a photo tech in a shop would get you better results I think.