I've only done it once and I don't know what the proper terms are so bear with me.
I had a Wenonah Vagabond. The bow had a wooden brace (thwart?) across the gunwale instead of a large deckplate. I tied a soft shackle (loop) that would hang over the side and nearly touch the water. Then I clipped a biner to it and ran my anchor line through the biner. It acts like a pulley so the ropes don't cut one another if you run the anchor line through the soft shackle. I secured the other end to the thwart in front of me with what I call a slip knot after I let it out or pulled it up. I'm always facing into wind this way. Do the same thing behind and you'll have the wind at your back. You can reach out with your paddle and scoop the anchor up and into the boat or just pull it tight and secure it so the anchor is out of water when you're moving.
That's how I've always done it my kayak, only I use the carry handles instead of the soft shackle and a jam cleat instead of the thwart.
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With my Merlin (solo cedar strip) I just tie off to the seat. If it's windy or I'm in current that can get a bit tippy and I'll tie off to the rear thwart instead. I also don't bring an anchor, just a basketball net with one end tied off. Fill it with a couple of rocks and then clip a biner through all the loops on the other end and tie the rope to the biner.
On my magic I use two ropes. The anchor rope is thru a biner in the stern loop and tied off on the front thwart. The other rope is also tied to the anchor but that rope hangs over the side and is only used to pull the anchor up. I then pull in the anchor rope slack. Never had good luck trying to pull the anchor rope itself thru the biner w/o the assistance of the auxiliary rope. I like to anchor from the stern so I'm facing downwind. That way I'm not casting into the wind.
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