How to do minecraft multiplayer with a LAN cable?

I think you need atleast an router to set up a lan connection through hamachi for minecraft, but i might be wrong.

If you have a cable to connect you both you should be fine. One of you needs to make a normal world then hit escape and choose open to lan and then pick all the settings for your lan world. The other player just needs to start up their game and choose multiplayer and your lan world should show up for them to join.

On standard (rev b) RJ-45 terminated Cat 5e cable (what you most likely have) a PC would go through the to transmit lines (Tx) to the isp's reviving end. And the ISP would transmit to your receiving pair (Rx). What you need is called a crossover cable (rev a RJ45 Cat5e to rev b RJ45 Cat5e). This cable will cross the Tx lines from your PC to the Rx lines on your friends PC and vice versa (Tx>Rx).

While functionality to do this is built in to switches and routers, most user end machines still need these cables or an adapter to do host to host connections or client to client (what you are wanting to do) connections.