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Be confident with your strokes. Be careful, of course; but avoid being too apprehensive with the blade.
It takes a fair lack of judgment (or just simple inattention) to injure yourself with the razor.
I have only cut myself once in my three or four dozen straight razor shaves (and a minor cut at that), and it occurred because I was too shaky and inhibited, thinking more about how I would cut that little patch of stubble instead of, well, actually slicing through it.
That would be my advice.
Be methodical, be focused, but, above all, be deliberate too.
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Don't drink and shave...
:)
-Chief
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I have one HUGE piece of advice.
Relax.
That's probably the single most important thing. All of us here shave with a straight daily or almost daily, and countless millions of men have shaved with them over the centuries.
I have yet to find a single verifiable report of anyone suffering anything more serious than slicing their earlobe with a spike point while shaving, and since your razor isn't a spike point, you've got nothing to worry about there.
Relax, take your time, don't try to get a perfect shave at first, and keep the blade more flat than you think you need to. You can always increase the angle later.