Go to dyndns.com and read their help and faqs. They do this kind of thing for a living and helped me get my device on the internet. They used to have free accounts that you could get, but that's gone now. You can still get to their support and such to get information. There's another free service dnsquackie that is still free and has information on what you need, but I haven't used it yet.
The key to this is to find out your externally visible ip address. You can get that by going to http://checkip.dyndns.org
and looking at the page it gives back. Once you have that, you can use the address to access your house modem (cable, dsl, etc), but you'll have to go into the menus on the modem to allow access to a particular machine you have, but that differs for every modem out there. There's lots of help for this on the web, but you'll have to search for it. The last wrinkle is that the IP address you have will change over time and you have to keep checking it and doing whatever is necessary to set it back up. But, you'll learn about this stuff as you research the process.
No, I don't work for any of them.