Time Capsule is an airport extreme base station (802.11 a, b, g, n) with built-in hard drive for backup.
You set up the base station as usual, using AirPort Utility.
You can use your old base station to create a WDS network and extend your wifi coverage to attic or garden – or share with a neighbor. In any case, APPL say, you should make the Time Capsule your main base station – the one directly connected to your ISP.
If you just have 802.11n-capable access points you can let your network autoconfigure. Choose a common Network Name, Wireless Security and Password. Under Airport > Wireless set the main base station to Create a wireless network; set the other base stations to Extend a wireless network.
A domestic ISP typically gives you internet access via a single IP address. Depending on your ADSL or cable hardware you have various options for setting up your system to distribute local IP addresses to clients on your local network.
My ADSL modem is a speedtouch router. It provides a DHPC server with optional MAC authentication. WDS setup is simple: each base station is configured to get its own IP address as a DHCP client, and to act as a bridge passing wifi client traffic to and from the ADSL modem.
If your ADSL or cable modem isn't set up as a DHCP server, you can get the Time Capsule (or any Airport base station) to do this. Set the main base station to "Share a public IP Address" (under Internet).
If your modem provides a range of addresses that clients can select manually, you can set the main base station to distribute these. Select "Distribute a range of IP addresses."
Time Machine sometimes gets confused and can't mount the backup disk. Apple say the volume name should be shorter than 27 characters. Elsewhere they say it should be purely alphanumeric [0-9,a-z,A-Z]*