What should I do on Shabbat, if the synagogue is far away and I would like to go and pray there?

Good question. Though one may think that since it is for the sake of Shabbat, i.e. to go to the Synagogue to pray, one therefore may drive, Our sages in the Talmud teach us that we can't be cleverer than Hashem, so to speak, and if the Torah says you can't drive – it is better to stay home with no Tefilah than breaking Shabbat and driving to shul. All the best