Creationists (who are pure creationists rather than a blend of evolution/creation believers) tend to believe the world is somewhere between 6,000-10,000 years old. To address your cojoining question, they do believe in dinosaurs and such (it's not really optional, given the evidence, is it?) but their belief is that dinosaurs were created approximately the same time man was and that there was shared domain for a while. There are biblical texts that mention animals that could be construed as dinosaurs, so that contributes, but also if you include the flood as a consideration in your scientific examinings, there are scientists who have theories based on facts about the extinction and fossilization of dinosaurs.
For those of you with a bit of a blind belief in evolution-through-science (aka, believing what you read, since a few of you may have firsthand knowledge and the rest are going by trust in popular and accepted theories), there are quandaries and foils for evolution, as well as scientific pieces of evidence that would point towards creation if one chooses to look at them that way, or we could theorize a third, unknown possibility altogether.
For example, I studied astronomy for a period and know the theories of the creation of the moon, the predominant theory being that an object roughly the size of Mars crashed into a young and largely liquid earth, tearing the object to pieces and leaving a piece in orbit around our planet. When scientists were first landing a craft on the moon, they were quite concerned about the dust buildup on the moon. You see, the moon has no atmosphere to speak of, and space junk would have built up at a rate of 1 inch every 10,000 years according to their calculations. By the age of the earth and moon, that should have made a significant and dangerous amount of dust. (For a sci fi book written about this before the moon landing, read Clarke's "A Fall of Moondust" and you'll see their concern.) They designed the moon lander with special "feet" to hopefully prevent it from sinking into the dust.
Measurements showed the moon to have 1/2-1 inch of dust in most places. This isn't a question raised in classrooms or public venues. We only hear science reported when they think they've made some progress, not when there are outstanding questions.
There's evidence for both theories, depending on where you look, and both sides have VIABLE evidence for their theories. We don't have a full picture painted by the evidence yet.