Save as CMYK (EDIT: I should clarify saving as CMYK - this can be done, it's a pain in the butt to explain how to do it and create separations. You would have to make spot color channels, save those out separately to create true spot colors). Save as PSD that would be okay, but I think your bigger problem is actually that he's working in vector and you are working in raster. Maybe consider working with a different printer, one that can work in the format that you are working in.
You can have this printed digitally instead of having separations made. The question is, what kind of print run are you thinking of doing? Are you talking thousands of shirts? Hundreds?
If hundreds, maybe digital is the best way to go. Otherwise, you are probably looking at reworking your artwork to fit with what this printer is doing. See below for what would probably need to be done if you are talking about a higher print run...
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First, PNG isn't really a format that a printer will use for printing. It's more for on-screen use, like the web.
Your file is going to be a difficult one since we can't see it right now.
What he means by having it as spot color (and he isn't really helping explain what he wants) is it needs to have been vector art to begin with and be assigned either premixed colors that he as a screen printer would have in his shop or Pantone (PMS) colors for him to print.
Not sure if you had talked to him before you sent files, but he should have told you that he needed vector files first. Even if you didn't do the spot colors, he would have been able to make the changes to the file to create the "spot" colors which would allow him to assign colors to each area of the image.
With a raster file, unless you have straight flat colored areas, you won't be able to make these into spot colors. These would be continuous tone like you would have in a photograph and would be basically impossible to convert to spot unless you make them black and white first and convert to spot.
Your file, being a raster file in Photoshop could be made into spot colors if you isolate the solid colors, put the same colors on one layer, make the the color patches black, go to your color palette and fill with the Pantone (PMS) color and dump in the color you choose, or you can just give him the file with the black layers and tell him what color you want each layer to be.
You also need to know what Pantone or premixed color he can reproduce, so you need to talk to the guy about that. There are a bunch of Pantone colors palettes out there, make sure you pick the right one (more than likely the PMS uncoated).
Hope this helps!