It would require, you see, a number of beans (the precise number to be determined).
The beanstalks would be placed at even intervals and allowed to grow to their full height. At the top of the beanstalks a platform would be erected, upon which copious amounts of dirt would be placed. Then, a smaller number of beanstalks would be grown, again placed at even intervals. This would continue for as many iterations as necessary.
Eventually, the last of the beanstalks would terminate in an orbiting space station.
Travel up and down the beanstalks would be through a series of pulley systems. Or, if you will, elevators.
Although the concept of a space escalator is also attractive.