The trick for doing the stars is this: Put a blob on the star, big enough that the surface tension makes it, well, blobby... do the same on the ground ring. Let it cool, then with just the very tippy tip of the iron, lightly touch the top of the blob on the star, pull the iron across to the blob on the ground ring, and then pull the iron away. Do it in one smooth continuous motion - if you completely melt either blob, it won't work.
I think he wanted to know how to attach the braid to the top of the board without the whole length sucking up the solder. But after that, I agree…flux,flux,flux. Before I push the driver into the pill, I flux the braid, even though it comes pre-impregnated.
The last batch of 'Goot Wick' I got claims to be fluxed, but... I guarantee you, it is not. Which is fine, really, as it can be used for stuff where flux would have to be washed out (braiding springs etc.), and flux can be added when it is needed. And by adding flux you can control where/how much is impregnated with solder.
I find the solder-only method of bridging the stars easier, as compared to trying to keep a small piece of wire in place. I always end up with the wire stuck to the tip of the iron (d'oh!). Might go smoother if I used a long piece of wire that's easily held in place and then trimming off the excess at the edge of the pill, but I have the blob-to-blob method down pat.
You can still bend the braid over without lifting any traces if it sucks up too much solder, just hold it flat to the board with needlenose pliers, then bend it over the corner.