Newtons laws and Einstein's theories contradict

Newton's Laws are known as the "slow speed" approximation of physical laws (they are also the "large scale" approximation- we talk about this when we are discussing how they contradict Quantum Mechanics). What is important to remember, it isn't that Newton's Laws are "wrong" and Einstein's Laws are "right." Both sets of laws are mathematical models of what actually happens, and Einstein's Laws cover a wider variety of cases than Newton's Laws, but they are still a model, which does not perfectly predict all situations.

Now, as for the differences, Newton's Laws explain what happens when large things move slowly (large being relative, even a tiny ball bearing follow Newton's Laws almost perfectly- here large means "more than a few million atoms"). What Einstein predicted, and has been backed up by many experiments, is that light moves the same speed in any reference frame, and that nothing can go faster than light. Turns out, this has all sorts of odd implications, including time dilation (time appears to travel slower for someone going faster), length contraction (an object going faster measures distance to objects as shorter than an object going slower), and velocities are no longer additive. But you can only ever see these effects when you are going really, really fast.

So it isn't so much that Newton and Einstein "contradict" as much as it is you can only use Newton's Laws when you are a big object going slow. You can say that Einstein's Laws (which are very difficult to work with, and require a lot of calculation) simplify to Newton's Laws in the big object going slow limit. So, if you have an object going really fast, Newton's Laws will no longer work to accurately predict what those objects will do- not so much because they are "wrong" but because we are outside of their realm of validity.

Remember aswell that under newtons laws, if lets say, the sun dissaapeared out of existance, according to newton the earth would fly off on a tangent. Because of einsteins model of it we know that it would take 8 minutes, or the time for light to travel from the sun to the earth for this to happen.

This is actually an inaccurate oversimplification: Einstein's General Relativity provides corrections for Newtonian gravity, and this is useful from scales of the solar system right through to the cosmos.

This is actually an inaccurate oversimplification: Einstein's General Relativity provides corrections for Newtonian gravity, and this is useful from scales of the solar system right through to the cosmos.

This response is focused on the quantum aspects of the differences between the two theorists, probably a result of OP asking a rather broad question!
However, it's still inaccurate to focus on the scale: we have already made very large scale (~km) quantum objects.

As others here have pointed out the thought experiment of the sun disappearing is probably the most well known and easy to understand way of showing the difference.

Newtonian physics allows for the propagation of disturbances or forces without regard to the distance between the bodies in question. What this ends up doing is allowing for instant transmission of forces like gravity.

Einstein on the other hand was able to find out no disturbance can propagate faster than the speed of light. Meaning that , like in the scenario with the dissapearing sun, we here on earth would not know of the disappearance of the sun until the light containing that information reached us.

There are other differences as well.

Newton did not make too much of an attempt to explain the cause of gravity, considering it an inviolable law of nature, something that simply exists in-and-of itself without the need of any progenation. In short, in Newton's mind, forces like gravity are first principles.

Einstein on the other hand stated that gravity is the effect and not the actor. He postulated with amazing accuracy that gravity is the warping of the fabric of space and time. The net effect of this is the understanding that what we feel as gravity is really the reaction our bodies feel when we move through curved spacetime.

Newton also felt that time was a first principle much like gravity and as such that time moved identically for all observers regardless of the frame of reference.

Einstein showed that, indeed, the flow of time does change when the frame of reference changes. Moreover he was able to predict the amount of change and his predictions have been verified by our best experimental evidence and calculations.

While Einstein's theories more accurately describe the world we live in, it should not diminish the amazing contributions made to mankind by Sir Isaac Newton. Newton's mind and his ability to analyse and solve problems are rightly the stuff of legend and the world had to wait hundreds of years before another individual rose to stand with him in the pantheon of great scientific minds.