I only have done this in one direction, on board ship you would do this left-handed where required, I only know right-handed.
With the line to be belayed in your left hand, holding tension, take the tail in your right and pass it behind and below the pin, right to left. Pass it again, without letting go, behind and above the pin, right to left. That's the figure-eight. You can probably let go with your left hand now, there should be enough friction to hold it secure. Still with your right hand, pass the tail again behind and below the pin right to left, then bring it up and throw a loop which you put over the top of the pin, with the loop crossing itself, a half-hitch I suppose it is. That's the line belayed. It shouldn't be going anywhere. Now you coil the remainder of the tail over the pin, (would be nice to keep the coils off the deck so you can swab and holystone under when you get up tomorrow, so keep them short). When you have the line coiled nicely, lift the coil off the pin with your left hand and, reaching through the center of the coiled line with your right hand, grab the first loop you made and pull it back to you, looping it up and over the pin. When you let go, the whole coil should hang from that first loop. Sounds too good to be true, I know, but it works, and I did this working in the theater in school where our 'line' was a line set of four 3/4" hemp lines. When you want to work the line again, lift the coil enough to free that last loop and drop the mass of line on your feet. It will almost always lift off the coil with no tangles.
There's a Nautical Research Guild shop note by Gene Larson with some photos of lines belayed in just this manner, very clear to see what has been done.
To address the cleat/bitts part of the question-- I have some photos taken on
board H M Bark Endeavour, and the variety of places used to belay lines is
wonderful to behold. Sorry, I can't scan them to share, but there probably are
photos on various museum vessel websites showing variations of the same
technique. On board Endeavour are lines belayed to pin rails, to cleats- on
masts, the bowsprit, the belfry, on the timberheads-, and one, I take it to be
the fall of a tackle hanging from the main mast, is coiled then secured to the
tackle above the block with a length of small line. If you wish to guess at
this last, she's in port with all sails tightly furled. There are multiple
lines belayed one on top of another on the same pin or cleat. There are lines
tied off to the timberheads and there is a gun secured to the open rail. In
every case, where there is much line left over, that line is coiled and hung
over the belaying point as I describe. Doing it that way means you use as
little of the pin as possible so you can belay another line or two at the same
point. If you merely left all your coils hanging on the pin, as you coiled
them, you would take up all the length of the pin with your coil. As to
belaying to a plain rail, without benefit of pin or cleat, I would be guessing.
I'll leave that one to those more knowledgeable than I.
{J B Sanborn}
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