How to make a black and white photo with color using a computer?

If you have a photo editing program on your computer, it should have an option to "grayscale" a picture. Look in the help file of the program for the Word grayscale.

That will convert a color photo into black and white (with various shades of gray -- called "grayscale").

If by "black and white with color", you mean mostly grayscale and some parts colored, there are a few variations.

One is sometimes called "selective colorization." That's where some of the color of the original color photo is preserved and the rest is black and white. The capabilities of image editors vary, but the page at the related link provided below describes how to achieve selective colorization using "gimp" (Graphical Image Manipulation Program) -- available for free through the web. The concepts described should be applicable to other reasonably sophisticated image editors as well.

Another way to make black and white images with some color is by, essentially, coloring over a black and white image by hand using your computer. A related page (link provided below) describes how to achieve that in gimp. Other sophisticated image editors should be able to do the same in a generally similar manner.

If you do not have a computer, you could hand-colour your black and white photograph using appropriate paint and brushes.