Hi,
You have a few options here.
A) If you have two Ethernet/Fast Ethernet interfaces you could configure 1 interface with an address from one subnet, and the other interface with an address from the other, and connect each of your networks to the router. This could be done using the same switch and having seperate VLANs one for each subnet or you could have seperate physical switches...
e.g.
router
------
interface fastethernet 0/0
ip address 1.1.1.1 255.255.255.0
interface fastethernet 0/1
ip address 2.2.2.1 255.255.255.0
B) If you have a flat network with no VLANs you could use a single interface on your router with a primary address in one subnet and a secondary address in the other subnet.
e.g.
interface fastethernet 0/0
ip address 1.1.1.1 255.255.255.0
ip address 2.2.2.1 255.255.255.0 secondary
C) If you are using VLANs and only have a single router interface available, plus your router and switch supports trunking you could trunk the VLANs to your router from your switch
e.g.
switch
------
Int fastEthernet 0/1
switchport access vlan 999
switchport mode trunk
switchport trunk encapsulation dot1q
switchport trunk alloweved vlans 2,3
switchport trunk native vlan 2
router
------
interface fastethernet 0/0
no ip address
interface fastethernet 0/0.2
description vlan2
encapsulation dot1q 2 native
ip address 1.1.1.1 255.255.255.0
interface fastethernet 0/0.3
description vlan3
encapsulation dot1q 3
ip address 2.2.2.1 255.255.255.0
On all these examples the default gateway for your clients would be set to the routers interface address matching the subnet they are in.
Option B is normally used if you are migrating between address schemes, so i would say depending on your router/topology you would be looking at A or C
HTH
PD