Honestly, I would probably take it to a seamstress for the alteration. I've been sewing forever too.
But I hate hemming and this dress sounds a bit tricky. But if you want to try it yourself, I have some ideas.
First of all, if you can fudge the length a bit to give yourself room for a redo, I think that would be a good idea. Like plan to hem it 10 inches shorter instead of 12, so that if you mess up you can cut off the mistakes and try again.
Check out the hem currently on the dress. That is how much you will want to turn up for the hem. Figure how much to cut off. If the current hem is 1.5 inches wide and you want the dress to be 10 inches shorter, then the amount to cut off = 10in - 1.5in - 0.25 in (so you can tuck the raw edge under) = 8.25 in. Or whatever your measurements really say. You might want to adjust this if your dress has a slit or a button-down-the-front placket. You don't want to cut it off and leave a two inch placket or a button at the hemline, you know?
Mark a cutting line by measuring up with a ruler and putting a chalk mark. Do this every 2-3 inches around. Connect the marks with a smooth line. Double-check length. Cut.
I am assuming you do not have a serger. So turn the edge under 0.25 inches and sew it in place. A straight stitch on your machine is fine. Then turn it under the rest of the hem width and sew it in place. If the original hem looks like a straight stitch from the right side, then copy that. If not, you might want to handstitch it in place. Before you machine stitch, you might want to practice on the piece you cut off.
If your dress really is like the fabric in the picture, it is difficult to press with an iron. Just pressing as usual will make the velvet part flat. You might be able to press lightly with a towel, or another piece of velvet, or a special velvet pressing cloth.
It is really hard to be too specific with details without seeing the dress. Please, if you have more details or questions, post again. The dress sounds lovely.
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