how fast can a spaceship go and what method ?

For our current spaceships, and rocket technology,

perhaps we could achieve 300,000 miles per hour.

(which is about 3600 times slower than the speed of light.)

We currently achieve 30,000 miles per hour -- using a single rocket to lift the spaceship off earth's surface and give it its velocity.

Plus we use gravitational assists by passing close to a planet (eg Jupiter).

To get the higher speed that I am speaking of, the space craft would dock in earth orbit with a few booster rockets. The boosters would be bought up into earth orbit on separate rockets.

So then the spaceship is already traveling at orbital speed, then it uses half a dozen booster rockets to get a huge boost of speed.

Using that technique a spaceship could reach another star in 2 or 3 thousand years instead of 20,000 years.

Theoretically a ship cannot exceed the speed of light ..... BUT .... Aliens ,.. They cheat....Using a black hole , or a worm hole , then , I can't give you an estimate of how far they can travel or how fast.... Who knows?