Note that the machines this program constructs are somewhat different from the ones we use. In particular, they allow a single instruction both to write a new symbol and, optionally, to move the head. So instructions come in the form not of quadrupes but of quintuples: OLD STATE, SCANNED SYMBOL, WRITE/ERASE, LEFT/RIGHT/STAY, NEW STATE. But it is still useful for experimenting.
Exercises for Peter Smith's Introduction to Gödel's Theorems. These include answers and can be used for practice.
If you have not previously had any logic, you will need to do some catch-up along the way, and definitely when we get to that material. Here are some online textbooks, or something of the sort, that might help.