I use a cordless drill, a Dremel with a few different attachments, some strong 2 pck epoxy resin and a pair of pointy nose pliers.
I firstly cut off the old knot at the base with a cutting wheel on the Dremel. I makes very short work of it although the burning hair smell isn't too pleasant. I then drill 3 or 4 big holes into the old knot base. The knot will then mostly pull out with the pliers. I then tidy up the hole with a sanding drum on the Dremel and it's then ready to measure up for the new knot. If the hole is in between knot sizes, I'll bore it out further with the sanding drum. Then it's just a case of glueing a new knot in the hole. If the outside of the handle needs a polish I use a polishing wheel on the Dremel with some car paint cutting compound and polish.
If I can do it successfully, it really is easy. Just buy a couple of really cheap old brushes and have a go.
"Yes, Madam, I am drunk, and you are ugly. But in the morning, I will be sober and you will still be ugly."
Sir Winston Churchill