You will usually get a public, dynamically assigned, ip address that you can connect to from the 'net. Use something like the good old dyndns to find yourself from outside.
Some providers could assign you a non-internet-routable RFC1918 address, they'll do NAT for you in that case to let you surf the 'net but you won't be able to connect from the outside in that case. See Private Network. If that's the case, you need to initiate the connection from the inside to a known, reachable, outside address (ie, do things the other way round). There are 'hosted vpn' services out there (you connect both your home and your laptop to the (known, public) vpn server and the two will be able to communicate).