How to connect internet to a computer without an ethernet port?

My sister in law gave me her old computer (emphasis on the old). I definitely need to put in a new hard disk as the current one only hold almost 2 gb's, plus I was planning on putting in xp or vista. But I also noticed that on the back that there is no ethernet port like my current new computer. Instead it has 2 ports for a phone cable, unlike my computer that has 1 phone cable port and 1 ethernet port. Does anybody know how to connect internet to a computer like this?