I have a watch and the wristband is breaking apart. It seems there is no easy way to attach a new wristband to the watch. What are some alternatives to fix the wristband of the watch?
The plastic that flexible things like wristwatch bands are made from is essentially impossible to glue together, because the oils that are milled into the plastic to render it pliable prevent glue from sticking to it.
Per MrWhite, check the wristband-to-watch joint for springpins, which allow the broken band pieces to be removed for replacement.
If your watch is such that the strap can not be replaced, you can cut the damaged bits off and replace the now missing bits with a fabric, leather or knotted replacement.
To attach a replacement bit of strap you likely want to 'drill' holes in the end of the strap, far enough from the actual edge that the holes do not tear out. You can now sew the replacement to the holes, likely easiest with holes in the replacement leather, or just into the fabric.
The most 'need to know how to do it' but best looking if done right might be to tie string to the holes and macrame the strap replacement.
But if at all possible, I would replace the strap, either with a factory made or a home made replacement.
As said in the early answer, most watches have a spring pin. Others work with holes in the watch case and a strap attached in some way to those holes.
Either one can be used to attach home made straps or 'a home made strap' but if you have a watch case with holes to attach the strap rather than the standard spring pin, you may have to use the same brand as the watch or make your own.
This is not the Stack Exchange site to detail how to make the straps.