NTM -> DTM Transformation?

I've been reading lately about non-deterministic Turing machines, and
everything I read says that for any NTM a comparable DTM exists (though
it may be horribly slow), and I'm just curious if there's a formal way
to transform a NTM to a DTM. Particularly, say I have an NTM with a
state A that when it reads a 1 loops back to itself (and writes
something to the tape, and moves the head), and but also has a
transition where it reads a 1, loops back to itself, but writes
something different to the tape and/or moves the head in the opposite
direction as the other transition. Thanks for any information.

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