First, let's start with the most common. The whip stitch. You just put two pieces right sides together, and then whip stitch using a matching thread. Positive--fast, easy. Negative--stitches show on front.
I don't like this method as I don't like the stitches to show.
I actually like to butt up my two pieces. I still whip stitch but if you hold them side by side instead of right sides together then your stitches won't show.
Positive: More durable than other stitches, threads won't show Negative: harder to 'get the hang of'
(I could not get the camera to focus and I looked all over the web and couldn't find a freebie photo or video,
but you just 'butt' the sides together.)
My Sister is making a hexagon charm quilt right now.
Her preferred method is actually a running stitch.
You really should Visit here to read how to do this method.
Another popular method that I haven't tried yet is the ladder stitch.
You can find a great tutorial of it over at A Few Scraps.
The tutorial states that you cannot see your stitches this way,
so it does intrigue me.
But, This post at Texas Freckles talks about how she has tried all of the methods and after sewing hundreds of hexagons, she feels that whip stitching will hold up the best.
Only she doesn't butt them up edge to edge.
AAARRRGGGHHH...You will just have to use your imagination,
or if you know of anyone that has a nice video of this method please share!