Now, you can see that how the handle has lengthened and thinned as I have smoothed and shaped it with my wet hand. At this point, you can add a groove with your thumb if you like that look. Don't be afraid to experiment! I almost always have an inch or two of clay to pinch off at the end. If you should need to reattach a new handle stub, scrape the top of the cup smooth and set it aside for a little while. The cup clay with be softened from the first attachment, and it will need to stiffen a bit. If the handle stub has been properly prepared, this shouldn't happen.
Here's the cup and handle ready to finish. You can see the nice taper that has been created by the wetting and smoothing process. There is also a taper in the other plane, but I didn't think to take a picture of it. Please note that the cup has been held parallel to the floor throughout this entire process. I find that this makes a smooth and attractive attachment point much easier to make.
Hold of the tail of your handle and give it a small tug to pull the handle down to the point of attachment. I score the bottom of the cup where the attachment will be made before I begin to wet and smooth the handle. Take special care that your handle is attached straight down - parallel to the long axis of the cup. I still have to really concentrate on this to make it right. The handle is pretty wet and weak at this point, and cannot be taken loose and moved, unless there is a lot of clay still in it that can be pulled down in a second effort.