First of all, you must configure all 3 VLANs on all Switches. After that you can deploy the trunking ports configuration:
Switch3: int fa0/5
Switchport mode trunk
Switchport allowed vlan 1-3
Switch2: int fa0/4
Switchport mode trunk
Switchport allowed vlan 1-3
Switch2: int fa0/1
Switchport mode trunk
Switchport allowed vlan 1-3
Switch1: int fa0/2
Switchport mode trunk
Switchport allowed vlan 1-3
I suppose that the Router R2 work like router on a stick ?
Switch1: int fa0/3
Switchport mode trunk
Switchport allowed vlan 1-3
Cisco 2960 supports only IEEE 802.1Q trunking methods for sending VLAN traffic over Ethernet ports