the trick to getting your binding to lay perfectly flat is to fold it AHEAD of where you are working...fold smooth over the seam, smooth to the edge, smoothly around...STRAIGHT around the edge...no scooting to take slack out above where you are working, if there is ANY slack, it needs to be stitched out now....
now pin or clip with the hair clips mentioned above or a pin or two... i just do 2 or three 3" sections at a time and then blindstitch these...but BEFORE taking off the last clip...make your new folds and clip...moving that fabric at a 90 degree angle around the edge is THE key and most people that have problems with binding find this is the root ... scooting the slack down the quilt as you work just gets further and further off...
ending the binding? easy-peasy..... this happens on the first round of stitching, usually by machine on the front side... begin the binding a few inches away from a corner, not the middle and not a corner.... matching the raw edges together, leave 4-6 inches unattached...pin/clip the first 2 or 3 sections....NOW go back to the loose end. with raw edges to the right, and loose end above, put your right thumbnail RIGHT ON the first pin and hold firmly...use left hand to fold the loose end down on a 45 degree fold, the loose end will be straight across the binding (exactly perpendicular) and the fold will be on the bias (the 45 degree fold).... begin your machine stitching where the folded join meets the quilt, at the appropriate spot for your particular binding width.
you will sew all round the quilt making the right kind of corners when you get to them... and when you are coming back to the beginning, you will lay the end of the binding over the original bias fold, pushing the top pc of binding just a tiny bit to the inside of the first pc. this is just so when they fold they come out the same... i'm talking about 1/16"... just a smidge.... this end goes approx 2 in past the low point of the bias fold. After folding to the back and making as flat as possible, then you will trim the extra that was only left there so you had a little 'handle' to work with. when you do the second half of the binding by hand, it will appear that you have made a bias join, the seam will be flat, look great and there is no real reason to even close the little opening but many of my students do. i don't bother, the finished edges are well away from the opening and i make my binding 1/2" wide so it never shows....