By default the wireless routers are configured with NAT and DHCP enabled.
Your wireless adaptor's IP settings should be assigned in such a way that the IP and DNS server addresses are automatically obtained.
This way once a user is connected to a wireless router, his system will be automatically assigned the private IP, DNS and default gateway by the wireless router. There is no need to assign them manually.
If you assign them manually you will have trouble connecting to one of the network whose IP, DNS, default gateway addresses are different.
When you are at home and connected to your home network,
1. Go to control panel - network and internet - manage wireless networks. You will see your adapter connected to your home network.
2. Open Adapter properties, double click on Internet Protocol version 4 (TCP/IPv4), select Obtain an IP address automatically and Obtain a DNS server address automatically. Ignore any values you may see in the fields. They will be deleted. (This setting you have to do only once)
3. Right click on your home network and select properties.
4. Select connection tab, put a check mark on "Connect automatically when this network in in range" and "Connect even if the network is not broadcasting its name (SSID)".
5. In the Security tab select the security type, encryption type and enter the Network security key (password).
Repeat the above 4 steps (ignore step 2 second time) when you are connected to your office wireless network.
This way you will connect to the respective networks automatically whenever your computer is in the wireless router's range.