Connecting a Layer 3 Switch to a Router

On a Layer 3 Switch you can change a Switching Port to a Routing Port with the 

no switchport command

Then the interface can be configured with an IPv4 configuration to connect to a router or another Layer 3 switch

If VLANs are to be reachable by other Layer 3 devices (Like Routers), then they must be advertised using static or dynamic routing

To enable routing on a Layer 3 switch, a routed port must be configured

interface ethernet 1/3

description to Border Router

no switchport

ip address 10.0.0.1/30

no shutdown