Both the young earth creationists (YECs) and the old earth creationists (OECs) generally believe God created the universe and the earth as set out in the first chapter of Genesis, although you will find some differences of opinion in both groups.
Although the YECs may differ among themselves as to how many of the assumptions made by Ussher and Lightfoot they believe (which causes their estimates of the age of the universe to run from about 6000 years to about 58,000 years), they tend to be united in their belief that the Hebrew word transliterated as yom should only be interpreted to mean a 24-hour day. They reject the other meanings for yom primarily because that is the most common usage of the word and because of the repeated usage of the phrase that concludes each of the six days of creation: (with the Hebrew words reversed to correspond to the English order) wayhi-'erev wayhi-voqer yom 'echadh....yom sheni....yom shelishi...., which is generally translated "and it was evening and it was morning day one....day second....day third," etc. (which they say clearly show a regular 24-hour day).
The OECs also have their divisions, with the major division probably being between the ones who accept a literal reading of Genesis and those who prefer a figurative or nonliteral reading. Both groups tend to remind the YECs that since the sun doesn't show up until the fourth yom and since it is not certain the Earth has been formed until the third yom, a 24-hour day is questionable. Additionally, the group favoring a figurative interpretation generally assert that the Bible's account of creation is intended to be read figuratively instead of literally. They say the Bible is a spiritual guide, not a science book, and the purpose of its creation account is to say that God created the universe and cares about our spiritual needs.
The OEC literalists generally point out that the Hebrew word for day (yom) can mean an indefinite period of time. Thus, they generally contend that each day of creation was of an indefinite period of time (even millions or billions of years) and we shouldnt get caught up in insisting that the Bible means something here that it probably does not mean. They also respond to the YECs' "evening and morning" argument by pointing out that the Hebrew usage of the words can (and probably do) indicate during each successive yom, God was bringing greater order out of chaos.
The Bible can support any of these positions--and they are discussed and debated in much greater detail in various threads and polls in this forum.