I would NEVER wean earlier than two months. Three months is ideal if you have the milk. The development of the rumen is not an overnight process, many people see a kid eat a stem of hay and make the mistake of thinking the kid is ready to live on it's own. In truth, the rumen begins working and increases capacity very gradually, eventually the groove that transports milk through the rumen to the true stomach disappears, and THEN the kid is ready to be weaned, but this process isn't visible so it's not an exact science.
Kids can survive weaning from several weeks on, but that doesn't mean it's best for them. If you wean at two months you will probably see a bit of "post weaning slump", that is a period of non-growth (and possible weight loss) followed by a gradual return to growth. At three months, this is much less a problem and the kid has had an additional month of rumen development and will be eating much more. Some people that have a lot of extra milk keep feeding their kids because they have other real use for it. The longer you keep feeding milk, generally the better/faster your growth will be, but for me, bottle feeding for more than three months was just impractical and I felt they were far enough along that they did well weaned at that age. If you have the milk and the time, five to six months is acceptable. However, a lot of babies will self wean after the third or fourth month, when a kid does that it's safe to assume it's ready to wean.
Start by cutting the middle feeding, then, when you are closer to weaning age, go to one feeding a day, then stop. Do not feed water in a bottle, goats need to learn to drink water from a bucket. The only time I feed liquid other than milk in a bottle is if the kid needs some kind of medicine or is dehydrated.
This is what I do, and it is by no means the only way to raise kids. I would advise you to listen to what everyone has to say, choose what makes sense to you, and go from there. A lot of raising goats is tailoring it to fit you and your individual needs.