Ok, so how I understand it, you both have a laptop that is capable of Wi-Fi and lan connections. Most importantly, do these co-op games support "LAN" (Local Area Network) options? If the answer to the previous question is no, than you will need to play with each other with an internet connection. If the games you are playing to play do support "LAN" options, then their are several methods you can use to get what you want done.
As Demonslayer has already previously stated, you can use a Crossover cable to connect both of the laptops to each other so that they can communicate with one another. The other option is to use a Switch/Hub/Router. The other method, depending on if you have a Wireless Router, may require you to have two Cat5e / Cat6 Ethernet/Networking cables. If you have a wireless router, you can both connect to the device without having to worry about the length of cable you have limiting you to too where you sit / stay with your Laptop. All three of these options Crossover Cable, Wired Router/Switch/Hub, Wireless Router, will require that you at least have some knowledge of how to setup a network. You could probably google and simple setup guides.
Since I am all the way on the other side of the internet, and I am unable to see what devices / equipment you have, it will be difficult for me to tell you exactly what to do but I will try. FYI, if you didn't know, I'm currently getting my degree in Computer Science and will soon be working towards becoming a "Bachelor of Computer Science" with my specialty being Computer Networking. What you what is really simple and I network computers all the time for clients. If you lived near by I could totally set it up for you. But I doubt you live in Houston, Texas
Note: Co-Op Offline is what I like to call, what people used to do before internet gaming became huge. No seriously, LAN (Local Area Network) parties were a big thing and still are today.