convert photo into shirt design?

I am making a shirt design for class. I have a picture of a dog in which I want to put on the shirt. Since I am not doing iron ons and using a company to make the shirts, I need to make the picture into less colors to make it cheaper to print. Is there a program or a way to where I can convert a picture into a less detailed picture so I can send it to the company to print out?
I have photoshop

Is this is a detailed photo or something that is very basic? If it's the latter, you'll want to convert the image to vector format using Illustrator or another similar program and save it as an SVG file.

It kind of depends on the photograph. I think it would be easier to just illustrate the photograph because then you can control the amount of detail and colors in the artwork for the t-shirt.

Like Xanis already suggested that you use illustrator to do a vector illustration. I would probably go about doing the same thing, or the same process in general.