If you just do what Verte said, which is the simple way, it will work for the most part, but it's not the right way to do it. You will end up with network address translation (NAT) occuring twice, which will make manual port forwarding a nightmare and UPnP port forwarding not work at all. Many applications won't be affected (e.g. web browsers), but others will.
A better way to do it is using a
wireless range extender. This is a different device although they look a lot like a router, cost about the same, and are made by all the same manufacturers. The advantage of extenders is that they are fully transparent -- you won't need to connect to a different wireless network outside, it will just work uninterrupted as you move around.
It is also possible to do it your way and avoid the double NAT issues if you use an
access point (WAP) instead of a router for the second device. A WAP is only a wireless bridge and does not route, so it is actually a simpler device than wireless routers (which are a router + WAP). Once again, all the same manufacturers offer WAPs. If you do this, moving between the devices won't be seamless and you need to set one up for channel 1 and the other for channel 11 (or higher, if available in your country), to avoid mutual interference.
If you already have a router you want to use, it can be configured to act as a simple WAP. To do that, disable the router's DHCP server and connect the uplink to one of the LAN ports, instead of the WAN port. If you need any help with that, feel free to PM me your Messenger address and we will find some time to do that.
Overall, my recommendation would be to buy an extender.
