Space is big. Very big indeed! Space travel is generally considered to be travel between one planet and another regardless of whether those planets are in the same Solar System or ones separated by the width of the Galaxy. The former is (barely) within present technology whilst the latter in any realistic form is not. In Science Fiction, the commonest method of travelling between the stars is travelling through hyperspace. This is basically a handwaving exercise to let the author get around the light speed barrier. Other methods of space ships that get covered quite well are near light speed vessels that depend on the Einsteinian time contractions that occur at very high velocities. Societies that are built round this sort of travel include the Ender series by Orson Scott Card and the Ekuman (or Hainish) series by Ursula Le Guin. If you have Excel 97 or better click here to see what happens at various near-light speeds. Generation ships are another common method of travel. These involve a very large space ship or a hollowed out asteroid travelling at fairly slow speeds where multiple generations are expected to live out their lives on the journey. Often, the story in these cases revolves round such ships that have suffered some form of rebellion or catastrophic failure and the colonists have forgotten that their world is in fact artificial. One of the classics of the 'lost Generation Ship' is Non-Stop by Brian Aldiss. A further method of overcoming the huge distances between the stars is the use of cryogenics.
See here for an article on starships
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