Longer than the age of the universe if we're using modern technology. Things in space are very far away, the closest galaxy being about 2.5 million light years away. So what a light year is, is the distance that light travels in a year. Light travels at 300,000,000 m/s, so we would have to be going that fast to reach Andromeda in 2.5 million years. Obviously we don't have the ability to go even a good sized fraction of that speed, so it would take us billions of years. In order to travel intergalactically, we need to find a means of working around the laws of physics.