Strictly speaking, you can't link systems like that. The TRS-80 is a totally different architecture than IBM-compatible PCs, and the two won't "understand" each other. Given special software, you can use a serial cable link (typically a DB9 connector) to transfer data, as Nigel Goodwin noted; but that may not be as easy as it sounds, I'm not sure of the availability of Tandy-compatible file transfer software anymore.
An emulator/ROM setup is probably the easiest way to go. Short of building a cartridge reader that your PC will understand, or actually doing a complete Z80-based clone computer, there's not too much you can do. I'd recommend finding a community experienced in TRS-80 emulation, they can probably help you get things working.