With 2 ports, you can use a technique called "link aggregation" or "bonding" which makes the 2 ports look just like 1 regular port to the applications you are running. There are pros and cons to this:
Pro:
1. Better fault tolerance - this was the original intent of the technology
2. Allows load balancing between 2 networks (E.g. cable + DSL)
3. Better theoretical speed (though you will be limited by the slowest part of your connection path).
Cons:
1. Puts your network adapter in "promiscuous mode", which means it will have to look at all packets sent on the network, not just packets sent to it - this means more load on the CPU
2. Your speed is still limited by the slower part of your connection path. For instance, if your internet service provide is only giving you 40Mb/second, you can't connect to the internet any faster than that by using 2 ports.
If you have 2 computers in the same room, each with 2 gigabit ports, and you connect them all up via a gigabit router, then you should be able to get nearly twice the transfer speed compared to using only 1 gigabit port. In this case, your connection speed to the internet is not a limiting factor.
You did not say what operating system you are running. The instructions will be different for different operating systems.
In most newer versions of Windows, for instance, just use ethernet cables to connect both ports to your router, then go to the control panel and right click on the network adapter and choose "bond".
See the links below for more info.