Unlike with dialup where you can sign up with the new ISP first and check that you can dial in to them successfully first before cancelling your old provider, broadband provides the one always on connection so that you need to have the old ISP disconnected first before you can connect to the new ISP.
I don't know if this applies everywhere in the world but here in Australia most ISPs make it extremely easy to be able to switch from one ISP to another when you are using ADSL (1 or 2). With those that offer it you don't need to cancel your old plan before signing up for the new one, your new provider will cancel your old plan for you immediately after they switch your connection over so as to minimize your downtime during the transfer.
If you are using ADSL1 then this service is called Rapid Transfer and for ADSL2 it is called Fast Churn and you can use it only if both the old and new ISPs offer the service (which most do).
The way that it works is that you use the Rapid Transfer or Fast Churn option to sign up for the plan you require with the new ISP without cancelling your old ISP first. They will prepare to swap you over and will send you emails (and perhaps even letters) containing the information you will need to do the reconfiguration on your end to connect to the internet through them. When they actually make the change to your internet connection at their end your internet will stop working. You then simply update the configuration of your internet connection to set the new username and password required to connect to the new ISP (along with the IP addresses of the DNS if you are using ones supplied by an ISP rather than public ones). You should then be able to access the internet as before.
Your new ISP will notify your old ISP as soon as they have completed their part of the transfer that you are no longer using the service that you had from the old ISP.
Exactly what the old ISP will do at that point depends on what plan you were on with them and whether or not there was any time remaining on a fixed contract. If you had completed any fixed term contract with them then there shouldn't be any cancellation fee with the old ISP and they should refund any unused portion of the time you had paid them for. If you had not completed the contract period with them then there may be charges for early termination of your contract. You are probably best not transferring to a different ISP until such time as your contract with your existing ISP is over.
Exactly what the new ISP will charge for providing this service will depend on what contract and plan you are transferring to.
The last time tat I transferred between ISPs like this my old ISP refunded the payment for the outstanding period within a couple of days of the transfer and the new ISP did not charge any fees for doing the transfer because I agreed to a six month contract with them.
One other thing to note with this is that these rapid transfer processes only work for transferring from an ADSL1 plan at one ISP to an ADSL1 plan at a different ISP or from an ADSL2 plan to another ADSL2 plan. You can't use this method to transfer from ADSL1 to ADSL2 or any other sort of internet connection. You can change the connection speed and bandwidth allowance between your old and new plans during the move.
This article written by Stephen Chapman, Felgall Pty Ltd.