First of all, you must configure all 3 VLANs on all Switches. After that you can deploy the trunking ports configuration:<br/>

Switch3: int fa0/5 <br/>
Switchport mode trunk<br/>
Switchport allowed vlan 1-3<br/>
<br/>
Switch2: int fa0/4 <br/>
Switchport mode trunk<br/>
Switchport allowed vlan 1-3<br/>

Switch2: int fa0/1 <br/>
Switchport mode trunk<br/>
Switchport allowed vlan 1-3<br/>

Switch1: int fa0/2 <br/>
Switchport mode trunk<br/>
Switchport allowed vlan 1-3<br/>

I suppose that the Router R2 work like router on a stick ?<br/>

Switch1: int fa0/3 <br/>
Switchport mode trunk<br/>
Switchport allowed vlan 1-3<br/>

Cisco 2960 supports only IEEE 802.1Q trunking methods for sending VLAN traffic over Ethernet ports