To connect your router to your network with out losing your Internet connection will depend on what kind of modem your have. If you have a modem with a built in router in it you can connect it to one of the extra network ports on the modem.
However if your modem does not have a router built into it you will have to disconnect the modem for a short time to connect the router into the network.
Note if your have a modem with a router in it the best thing to do is let it keep assigning IP addresses and turn on the DHCP server in your router and use it just as wireless access point. To do this you will need to set it to the same IP group that you already have on your network. So example if your modem has an IP address of 192.168.5.1 you will want your router the routers IP address to 192.168.5.2. The third number section is what is important. If you do not currently know the IP address of your modem and it is connected directly to your computer the link below will help you determine the IP address of the modem. The IP address listed as the gateway IP address should be the IP address to your modem. Note if you already have a router in your network this will be its IP address.
If you need more help and/or have trouble getting everything setup let me know the make and model of your network devices and how you have them connected so I can see what we need to do to get you setup with your new router.