I would not normally write such an article but I came across the same question from different sources with the same wrong answer twice in the last week.

The question was: I have bought a new wireless router and wish to connect my wireless laptop to the existing network? Obvious enough? Well not quite.

First choice (complicated)

What those asking me that question did was something similar to the following diagram:
Click for the original image
They had an existing network with the class 192.168.1.0/24 (LAN1) for example and wanted to plug the wireless router. What they did in fact was to plug the wireless router using the WAN port to which they gave an address in the 192.168.1.0/24 network. They then created a different network for the lan and wireless interface (which are usually bridged) say 192.168.2.0/24 (LAN2. This configuration causes that computers from LAN1 and LAN2 are not visible to each other and to make this visibility work you then have to add various routes all around. All in all this is mostly complicated and there is in fact a more simple solution.

Second choice (simple)

There is a more simple way which correspond to the following diagram:
Click for the original image
Instead of plugging the wireless router in LAN1 using the WAN interface you can connect using a LAN port. Usually you have 2-4 LAN ports which act like a network switch plus the bridge to the wireless network. This way your wireless devices are part of the LAN1 network and can use the same services such as the same DHCP server for address assignation. Most devices will require however to configure a static IP for the device itself. Usually all DHCP servers are configured for just a part of the available addresses so just use one outside the DHCP range to avoid conflicts.