How do I figure out the genotype and how to draw the Punnett square for this question?

I'm probably asking a completely idiotic question in response to your question and you may laugh, but do you not need to know what alleles are present in each animal and whether the dominant or recessive alleles cause the outcome?

One of the tan males was back-crossed to her mother (tan) and all their litter was tan.

Because all these babies were tan but the other crosses gave mixed color litters, black must be dominant (B) and tan must be recessive (b)

The original female was tan so her genotype was bb.

The orginal male was back so his genotype could be BB or Bb.

If his genotype was BB, all the babies of the first litter would have been black because the male could only contribute a B gene.

However, approx half the babies were black and approx half the babies were tan so the male must have contributed a tan gene, b.  Therefore, the original male's genotype was  Bb.

I can't draw a square here but here is an example that fits your problem. See:

http://hsc.csu.edu.au/biology/core/blueprint/2470/answer1.gif

which shows the female's genes down the side and the male's genes across the top.

From top to bottom, left to right you'd fill in the square with bB, bb, bB, bb

Good luck!

On the top you have Female and two