Hi Ian,
I'm assuming you have a working Model 1 or 3, which is hooked up to a standard tape recorder? I'm also assuming you know how to make your way around a disk based M1/MIII (like running programs etc.)?
Just how you transfer can depend if the game is in BASIC or machine code. It's easiest in BASIC.
(A) For BASIC
(i) Load BASIC and then load the game. Don't run the game though.
(ii) The interrupts need to be disabled, at least on the Model 1. I'm not sure about the Model III. At the BASIC prompt type 'CMD "T"' then press ENTER. (this is what I do with NEWDOS 80/V2 on the Model 1. I'm assuming it's the same in TRS-DOS)
(iii) With the tape recorder set up and ready to go type "CSAVE "<name of program>" then press return (replace <name of program> with the program name (6 or fewer characters)).
(B) For machine language programs
After loading the programs from disk, they are essentially held in memory somewhere above 5200H. You need to write out the block of memory containing the game plus a starting address. You'll need to have some kind of memory monitor program which will (a) Load in the game and tell you just where the game is loaded and where it starts and (b) will write it out to tape for you. I've used TASMON for this, at least on the Model 1. It can be tricky as TASMON must also be held in memory and it can't occupy the same space as the game.
You can pick up TASMON for Model 1 on a disk image
here (the manual is linked to that page also). You will need to move TASMON to a real machine of course. I'm not sure if TASMON for the Model 1 also works on a Model III.
Hope this helps.
Tez