What I have a problem with is that the Bible says that God created everything in 6 days and rested on the 7th. Is there any evidence for thousands/millions of years instead of 6 days? Let's start with that.
OK, lets start with that.
First, we have sedimentation rates. Observable today, sedimentation is a slow process that results in the gradual build up of strata of rocks containing period specific fossils over extremely long periods of time. These starta can be folded and ruptured by techtonic movements, and we see them move in ways in exactly the way they would move as predicted by this theory
Now, with in these layers, we find a timeline of fossils and datable minerals with standard halflives. Without exception, what are believed to be older forms are found lower in the strata than what are believed to be newer forms. This strongly suggests that strata atre laid down over time, rather than in one brief event, as the time line they show seems to cover a considerable period. If we were looking at strata laid down by one single flood event, we would expect to see all varieties of animals throughout all strata. However, what we see are earlier animals lower, and contemporary with the same groups of animals and time period through out the world, and more recent animals, also contemporary with others in later strata. I hope I am explaining this coherently, but I am a little pushed for space. If you would like direction to further reading on any of these points, just ask.
Anyway, observed sedimentation rates, tie in with elemental halflife dating, which tie in with advancing development of fossils through time, to strongly suggest that the earth is old, and the creatures on it have been devloping for a long time. Non of what apears in the geological record is what we would expect from a 6 day creation.
Then, to move out into the universe, and judge its age...
We know the speed of light,299792458 m / s. Scientifically, we call this "C" and it is always a constant when moving in space. Now, there is a thing called paralax. Basically, it is a form of trigonometry used for measuring distances. It is, essentially, the same process by which binocular vission allows us to measure distance. When used by astronomers with finely tuned instruments, it gives us a very good estimate of galactic distances, and those distances are VAST. By using paralax, and special stars called Cepheid variables, we are able to quite accurately ascertain the distances of objects really vast differences away. The point here, is that we know the speed of light, and we know that there are objects further away that light has taken more than 6000 years to travel across. This also strongly suggests that the universe is older than 6000 years.
If the universe were only 6000 years old, we should only be able to see for 6000 years in any direction, because light from further away simply hasn't had the time to reach us yet. But look up at night, and this is not what we see. Further, we see stars in the process of being made, burning, and dying, all before our telescopes, and across a huge range of time (i.e. further away, the longer ago, speed of light again, right?) and this again indicates more than 6000 years, and more than 6 days of creation. Otherwise all the stars would be about the same age, having been made within a six day period right? But again, thats not what we see.
So, theres a start. Lots of evidence for an older than 6000 year universe, and more than 6 days of creation, observable and repeatable and free to any one to verify all by themselves through simple experiments.
To continue to believe in 6 day, 6000 year old creation, means you have to start introducing "special" arrangements, like physical laws changing, and God creating things in such a way as to be deliberately misleading. Now, there is no way to prove that ISN'T what happened. However, how many special arrangements do you want to work into your theory of cosmology before it just gets silly? Especially when the simpler explaination requires NO special arrangements.
Would you like more information? Would you like more examples or details? Do you have any other specific questions about specifics of cosmology or evolution I can help yo with?