Yes, lots happens.
In brief…
There are two main parts to a Mass: Liturgy of the Word, and Liturgy of the Eucharist. This actually follows the practice of the early church, before they got kicked out of the temple. They would hear readings from scripture and a lesson from it, and then head over to someone’s home for Breaking of the Bread. The two parts merged into one about the time we began to be called Christians, and have stayed that way ever since.
For a typical Sunday Mass, there are the opening rites. Then a reading from the OT. A Psalm that is sung. A reading from the NT. Then the Gospel. So far we’ve heard from The Father and The Sun, on to the Holy Spirit, who hopefully has inspired the homilist to craft a good homily - sermon - that applies the readings to our lives.
Then we present our gifts - the collection plate, if you will - and our prayer intentions, and the bread and wine. The priest Confects the Eucharist, we have Communion. Usually some announcements, a blessing, and the closing hymn. Things are a little briefer on weekdays, some things get changed during Lent, and certain other Masses, like the Easter Vigil, have more going on.
I could go on and on and on, but others have done so before me, better. There are books about it and tons of apologetics websites, and even the catholic encyclopedia that has a tab at the very top of the page. You might try googling “order of mass” to get a full rundown. You can watch a Mass several places online.
thedailymass.com/mass.php is one. EWTN is another.
And you’re actually more than welcome to attend a Catholic Mass as an observer. If you’re in a big city, it’s especially easy to do so anonymously, since Catholics lag far behind Protestants in socializing and welcoming people. You can probably find an empty or nearly-empty pew, or if it’s crowded, stand against the back wall, and no one will talk to you at all.