Be sure to budget your time so that your poster is ready to print several days ahead of when you'll need it. Most printing options request at least two business days of time for large-format printing like posters, though they may also offer rush printing at a fee.
SCGraphics, in suite 013 of the Student Center's basement, offers large-format printing at very affordable rates and may also be able to provide some design assistance. Information on their hours and pricing can be found on their website.
Located in room 1367 of Scott Hall on the Med campus, Biomedical Communication is a design and digital imaging service open to WSU more broadly. They offer a variety of fee-based design services, and have an online portal for large-format printing requests. Information on their hours and pricing are available on their website.
With many design tools, you'll want to produce a PDF to send to the printing service.
You'll need to use the command
xelatex (which are included with most TeX distributions) to output a PDF file. For more information on this, consult the documentation for your particular TeX distribution.
Though Adobe Creative Suite tools can easily produce PDFs, many of their proprietary file types (such as .ai for Illustrator and .psd for photoshop) are usable on their own by printing services.
Another common file type used for design work is .eps, Encapsulated Post Script. Adobe Creative Suite tools can create .eps files, as can other design tools, such as Inkscape.