I read many guides saying something like this -

Let's add some flares, the flares I'm using is from this image http://www.williams.edu/astronomy/IAU_eclipses/jmp_eclipse03_04.jpg. After that resize the image and delete the other parts of it leaving just the flare itself.

How do I just save this flare, lol ?

Seen many guides saying just to save a flare / light / effect in a picture, but don't know how to render it so it looks good

Neither do I

right click > save image as

then open it up in the program your using and set it to a layer setting that just shows the brighter parts of the picture where the flare is (screen/add/lighten etc)