The two primary areas for concern when upgrading the network from 10Mbps to 100Mbps are cabling and hubs. As discussed on the Fast Ethernet Introduction page, in Fast Ethernet twisted pair cabling needs either to be category 5 or to be category 3 with proper twist on all four pairs.
The problem with hubs is the number of hubs allowed in a single collision domain. Classic Ethernet allows hubs to be cascaded up to four deep between any two stations. In Fast Ethernet, the number of hubs allowed in a collision domain is drastically reduced - to a single hub. Sometimes it may be possible to have more than one hub in a collision domain, but it will probably be easier in the long term to design a Fast Ethernet network assuming that only one hub is allowed.
What the IEEE 802.3 spec does not explicitly state is that this limitation only applies to shared 100BASE-T, not to switched 100BASE-T. Since switches act like bridges in defining a separate collision domain, installing Fast Ethernet switches will allow you to work around the single-hub problem. Even if it is not necessary to deliver dedicated switched Fast Ethernet to each desktop, Fast Ethernet hubs can be connected to switches. Connecting a number of repeaters to a switch will provide shared Fast Ethernet and allow you to maintain the size of your network.