I confess: I had to look this one up.
According to the Online Etymology Dictionary (http://www.etymonline.com/), the word soccer is a shorter form of "association", from the name of the Football Association. Speakers took "assoc", turned it into "soc", and added the informal "-er" suffix (you can also hear this in the way some people will call rubgy "rugger").
Football (which dates back to the early 15th century) is fairly obvious: you have a foot, you have a ball. Games like these date back to the Roman times; I like how the Online Etymology Dictionary points out that "[b]all-kicking games date back to the Roman legions, at least, but the sport seems to have risen to a national obsession in England, c.1630." (Some things never change.)
Hooligan dates back more than one hundred years:
...of unknown origin, first found in British newspaper police-court reports in the summer of 1898, almost certainly from the surname "Houlihan", supposedly from a lively family of that name in London (who figured in music hall songs of the decade). Internationalized 20c. in communist rhetoric as Rusian khuligan, opprobrium [=criticism] for "scofflaws, political dissenters, etc."
For more information on word origins connection with football/soccer/whatever you call it, look here: http://www.etymonline.com/index.php?search=soccer&searchmode=none.