What exactly do you mean with "internet security"? A firewall, virus scanner?
There are not that many virusses for linux but if you want to be sure, you could try ClamAv
A firewall comes built-in with the linux kernel (the core programme that runs the whole stuff on it and makes you use the hardware, i.e. dvd players, mouse, keyboard, monitor, etc.). But if you'd like to use a front-end, you could try Firestarter
, which is easy and quite nice. If you would like to know whether your firewall is working, type
in the console, provided that you know how to open one. Just press Alt+F2 and type xterm. You then get a screen where you can type the line above and then close it by hitting Enter. You should then see some output and then find out whether it is running (which it probably is).
Linux comes in different flavours, what distribution is pre-installed on your laptop: ubuntu, opensuse, fedora, ...? If you could tell us that, we could help and guide you through the installation steps more easily. Compiling from the source code works for all distributions, but it might be easier through a user interface if we know what distribution you use.
Enjoy the linux experience and ask questions if you have any.