In order to route between 2 VLAN's you need a layer 3 device. In this case you can use your 3750's by enabling routing. To enable routing type "ip routing" under global configuration.
You do not need any routing protocols (such as rip or EIGRP) if you are routing to only directly connected networks (IE: You put all three of those IP addresses on the same switch that you enable IP Routing on).
Don't forget to point your clients to the IP addresses of each VLAN's as a default gateway.
If you are trying to split those IP addresses between each switch, (IEL 10.10.10.1/24 on Switch 1 and 20.20.20.1/24 on Switch 2, you will need to enable a routing protocol such as RIP and advertise the networks.)
In order to do this the commands are as follows:
On Switch 1:
ip routing
router rip
version 2
network 10.0.0.0
On Switch 2:
ip routing
router rip
version 2
network 20.0.0.0
You can then view the routing information by issuing "show ip route"
Keep in mind that in order to use any other routing protocols on a 3750, you must be running an advanced IP services IOS.
HTH,
Craig