1. get a UBW32 for the CPU. plenty of online retailers for this.  proceed to step 2, or
2. get an Olimex Duinomite-mini (which I use), or Duinomite with the IO adapater (which I do not have, but reportedly it also works).  If you use these boards, you won't have to solder anything, but you will be limited to monochrome (small loss, as the TRS80 was monochrome, but I do like my green screen).  If you do this, you can skip ahead to step 3

get a UBW32-MCC for the jacks. assemble it. It's a fairly simple board. I do highly recommend buying a CR1616 solder tab (search 'gameboy' on ebay) battery that you can wrap in electrical tape and stuff underneath the mounted UBW32. Anyway, you'll need the connectors. The parts list enumerates the peculiar ones; the rest are commodity parts, so I didn't list them. Alternatively, you can make your own PCB, of course. Mostly, it just provides mounting for the connectors.

get a monitor. I am running just fine on a modern LCD flat panel

get a PS/2 PC keyboard. I have also successfully used one of those green USB keyboard-(or mouse)-to-PS2 adapters. I have /not/ successfully used that with a wireless keyboard. Maybe power, maybe protocol, dunno.  (I'm leaning towards protocol at this point, the adapter is rather dumb).

get a 2 GB microSD, FAT formatted. (I think 2 GB is the max the driver will support; haven't tested with larger. Anyway, I suspect 2GB might be able to hold all the software ever written for the TRS-80, ever.  UPDATE:  it works with up to 32 GB).  The file attached to this project can be decompressed to that disk to create all the needed directory structure.

burn the firmware. You can either download the source, install the compiler, and build it yourself, or you can take the file I have attached to the project, and in the 'doc' directory is the firmware HEX image. Also, a copy of the bootloader exe (for Windows) is in there. It's a HID-based bootloader, so you don't need drivers. It's so easy and intuitive, that I don't need to explain it, though note it was not linked to be able to run on XP, alas. I run it on 7 and 10 just fine. I think it's from the Schmalzhaus UBW32 project -- can't recall.

Boot it up, and watch it go. There's more doc in the 'doc' folder, with a little walk-through of running a program or two via the cassette emulation.

Profit! OK, maybe not-so-much, but you never know!