The last time we did it, the startup supplies from the Church were sent to the old stake president as soon as the change was approved and before it actually took place. So those supplies were available to the new stake the day of the division.
On the other hand, the FM Group never got word that the change was going to happen until one of the stakes told them. We put the new stake on one of the ward computers in the meetinghouse where the stake would be located until a new computer became available from the FM Group. Among other callings, I was the STS in both the old and new stakes, and have an excellent relationship with our FM Group, so the transition was not too difficult.
Another interesting part of the change was that the stake division was approved two weeks before our regularly scheduled general authority stake conference, and the change was made at that conference two weeks later. The entire conference had been planned with the general authority, who was not aware that a division was pending. Everything was replanned when approval came.
In addition, an Area Seventy was also assigned to the conference so that the General Authority Seventy would have someone with him to help make the change, although he could have done it alone if no one had been available to assist him.