If you are trying to change your Gateway IP, on Linksys you can do the following;
1) Login into your router
2) Go to "Status" --> "Router" (This should be on the main toolbar).
3) "DHCP release" will release your current Gateway IP
4) "DHCP renew" will reset and provide a new Gateway IP
To verify that your exposed IP is changed you can check many ways. (One way is to go to sites like WhatismyIP.com).
The above locations of the release/renew might be slightly different on your router dependant upon the firmware version. Even though I am on cable and you are on DSL, this should not make any difference, since its the routers interface.
Note: I haven't changed my IP often, so I don't know how your ISP will react to multiple changes. Tread softly.....
Hope this helps.