The Extraordinary Form of the Mass or Traditional Latin Mass has been in use in the Church since about the third century, so it is very ancient. It is the Mass that most of the saints throughout the history of the Church knew and prayed with. The Apostles themselves would have easily recognized it. In fact it has more in common with the Eastern Rites of the Church, both Catholic and Orthodox, than it does with the current and more common form.
What to Expect
Upon attending the Traditional Mass three things are noticed immediately.
First, that the priest faces the Altar most of the Mass.
It is not that the priest has "his back to the people." Rather, the priest is leading the people, the same people he himself is a part of, in prayer to Christ, Who is our focus. After all, no one would expect a bus driver to face the passengers while driving! The same way with the Mass. In fact the new Mass can be and often is celebrated this way as well.
Second, Holy Communion is received kneeling and on the tongue.
This is a physical gesture of receptiveness and humility, to Christ Who is truly and really present in the Host. It's a different way of receiving and eating a VERY different type of food. Since we cannot see with the eyes of our body What and Who it truly is, we need to use gestures to help remind ourselves. This is what receiving in this way does for us.
There is a lot of quiet in the Traditional Mass; especially a Low Mass (one without music). It can be stark even. But this serves a great purpose, that of helping us to LISTEN with the ears of the heart to the still quiet voice of God speaking deep within our soul. We live in a world of almost constant noise, but we read in Scripture: "be still (silent) and know that I Am God." The silence even within Mass helps us.
These are just a few of the most obvious noticeable things.