[wongarsu]

Getting from earth's surface to low earth orbit is about equivalent to accelerating by 9 km/s, in terms of fuel. Some it lost to drag and gravity, but at the orbit of the ISS you have an orbital sites of about 7.6 km/s.

If you could teleport a fully fueled Saturn V into orbit, it could speed up by about 18 km/s. More if you reduced the payload.

Of course going from 18 to 30 exposes you to the tyranny of the rocket equation: to go faster you need more fuel, which makes your rocket heavier, which means it needs more fuel, which makes your rocket heavier, ... Any small efficiency increase matters a lot here. It might be possible with today's tech if you build the rocket in orbit (which gets rid of aerodynamic constrains), or alternatively with orbital refueling and a couple more decades of progress in more efficient engine types (which you could greatly accelerate by throwing money at it).

[pfdietz]

Just using chemical rockets, speeds at infinity in excess of 100 km/s are possible using the Oberth effect: go into an elliptical orbit that passes close to the Sun, then accelerate at perihelion. Because the change in kinetic energy is thrust times velocity, and velocity is very high, large amounts of energy are added to the vehicle. The source of this energy is that the ejected propellant is left at low gravitational potential relative to where it was initially.

Solar sails released at perihelion can also achieve very high speeds.

Slowing down in the target system could be done with solar sails or electrodynamic sails (working on the stellar wind).

Ion or plasma engines are another possibility, with nuclear power plants.

[pdonis]

There is also the issue of losing speed as you climb up out of the Sun's gravity well. You gain some of it back by falling into the close approach star's gravity well, but from what I can tell, the close approach star is likely to be considerably less massive than the Sun, so you won't gain back all of what you lost. Which means you need even more rocket power.