Hi Geoff
there are a number of articles on this subject available from the web but initally it may be a good idea to understand the idea of escape velocity
http://en.wikipedia.org/wiki/Escape_velocity
simplisticly a space ship can accelerate and slow down, brake etc much like any other vehicle but this is very dependent upon the amount of fuel available to it
under constant acceleration over time an incredible amount of speed can be acheived but constant acceleration requires a vast amount of fuel current space ships don't have that luxury, so once a calculated velocity to reach a particualr target is acheived the ship would coast continually at that speed until its destination