After enabling ip routing on your layer3 switch the only other thing you will need to do is create Vlan Interfaces with IP addresses, and then set the PC’s / Servers and Phones to use their corresponding Vlan IP addresses as their default gateway.

So for example,
interface vlan 1
ip add 10.x.11.1 255.255.254.0 {or whatever IP address you wish to use}

Then all devices in Vlan 1 need to use the above IP address as their default gateway.
You would need to do this for all VLAN’s on the switch, then traffic will route between them.

Hope this helps.

If you had a multi layer switch (Layer 3 switch) then yes you could bypass the router all together.
So let’s look at that first, before we get into the second step of having a router connected to the internet as well.

On the switch you would require 2 VLAN interfaces, since the hosts in each VLAN still require a default gateway in their own subnet.
This can be achieved with the ‘interface vlan {vlan number}’ command, which will put you into the ‘virtual interface’ of the VLAN.
You could then attach an IP address to that interface, and do the same for your second VLAN as well
You then need to make sure that routing has been enabled on the multi layer switch with the command ‘ip routing’

At this point the hosts in VLAN 10 (as an example) would use the IP address of ‘interface vlan 10’ as their default gateway.
Hosts in VLAN 20 would use the IP address of ‘interface vlan 20’ as their default gateway, and traffic would be routed between the 2 VLANS.

Your second point was regarding DHCP on the router. You could actually configure this on the multi-layer switch as well, giving the switch the capabilities to issue IP addresses to the hosts, which is my preferred method.

So granting the users access to the internet would just involve a static route on the switch pointing to the internet router.
“ip route 0.0.0.0 0.0.0.0 {ip address of the router}”

Your last point, is to have the hosts accessible from the internet, this really depends on your internet service that you are using.
In order to have the hosts connect to the internet, NAT needs to be configured on the internet router to translate all internal addresses into a single (usually) IP address that is public (Often referred to as NAT overload or PAT). However, in order for the reverse to happen, each internal host requires its own public IP address, and this would be achieved using static NAT on the internet router to associate a public IP address to each of the internal hosts. This of course is only possible if you have multiple public addresses, and that depends on the type of service you have from your internet service provider.

Hope this helps out, and feel free to ask if any of the above needs clarification, or if I missed the point ?

Regards,
Jay

Single Router with Layer-3 Switch and with multiple LAN subnets

Internet
|
| 1.1.1.0/24
|
Internet Router
|
| 10.0.0.0/24
|
Layer-3 Switch
| | |
| LAN 2 |
| with UM |
| 10.0.2.0/24 |
| |
LAN 1 LAN 3
with UM with UM
10.0.1.0/24 10.0.3.0/24