This magnificent palace is easy to reach. Take the U-Bahn 4 to Schonbrunn. This was a summer palace and bears the most influence from Empress Maria Theresa (you'll hear about her everywhere - she was also the mother of Marie Antoinette of France, the one who lost her head during the French Revolution). This place is huge, though not as big as Versailles. However, we saw Schonbrunn first, so we were truly impressed.
You enter the grounds through a large gravel stone courtyard with a wonderful fountain on one side. Very grand entrance. I would recommend the Grand Tour, a longer tour than the Imperial Tour. Grand Tour takes you through 40 state rooms, including my personal highlights, private apartments of the Emperor and Empress, children's nursery, Hall of Mirrors (they said this is where the child Mozart first played for the Empress) and Napolean Room, where the great leader used to live and where his son died. Once you buy the ticket, you can only enter the palace at the stamped time. We had to wait about a half hour, which we spent outside wandering the gardens. Then, when you enter, remember to stop by on the right (before the stairs) to pick up a free audio-guide in your language.
Some rooms got really crowded-we arrived around 1pm so maybe that's a prime time for tours. There were a lot of European and Japanese tours, so just be patient and ease your way through. I found the Imperial Apartments quite a shock that the Emperor lived in such simple quarters. In such a grand space, he seemed to only occupy those two rooms. This is a must-see if you are in Vienna. If you've been to Versailles, then you may be disappointed. But bear in mind the extraordinary history behind this, and you will enjoy it just as much.