Problem with wired connection please help!

Hey guys got a problem i'm sure is simple but i cant work it out lol. So was woundering if some wise person could tell me what i'm doing wrong..
ive searched the forum but wired connections dont seem to be very common so cant find an answer.

Basically i have two computers and i want to connect over ethernet.
First is it possible?

secondly i tried setting static ips on both the computers but they still never connect! am i tryin somethin stupid or am i missing something??

Also what is the gateway ip all about?

You could start by giving us more details like what you tried, typed commands, the output ?
Do you want each of those 2 computers to be connected to the router or connect them between each other, etc.