How do I bind the new IPs I just purchased to my server's NIC?

Create /etc/sysconfig/network-scripts/ifcfg-interface-rangenum

For example if adding the first range to eth0:

vi /etc/sysconfig/network-scripts/ifcfg-eth0-range0
IPADDR_START=10.10.0.2
IPADDR_END=10.10.0.62
NETMASK=255.255.255.192 BROADCAST=10.10.0.63

This will create eth0:0 with the ipaddress of 10.10.0.2, eth0:1 with 10.10.0.3, etc.

To activate these changes do service network restart or just simply reboot the system.