When the priest celebrates Mass facing liturgical East, this is known as ad orientem.
When the priest celebrates Mass facing the people, this is known as versus populum.
As the missal contains instructions for both orientations, it is possible to celebrate the EF or the OF in each way. However, the vast majority of EF will be ad orientem, and the vast majority of OF are done versus populum.
In fact, I can guarantee that you will not find an EF celebrated versus populum, it’s simply unheard of. It may be that a particularly traditional-minded priest wants to celebrate the OF ad orientem. In these cases, you can probably expect it to be in Latin as well, and with various trappings such as incense and chanted propers. Ad orientem is not particularly an a la carte option, although by the instructions in the missal, it certainly could be!
Another way to find ad orientem liturgy is to seek out the Byzantine Rite. Preferably you could find one of the Eastern Catholic Churches in communion with Rome, but in a pinch, you could visit an Eastern Orthodox church. These liturgies are frequently done in the vernacular, sometimes with a bit of the church’s native language - you might hear Greek, or Old Church Slavonic, or Russian. You can receive Holy Communion in an Eastern Catholic Church, and you can even make it your weekly home parish without formally switching allegiance.
There are several other Rites used by Eastern Catholic Churches, and I am sure you can find ad orientem in most of them. It is the ancient way of celebration.
I am not sure if the fathers of Vatican II envisioned that versus populum would be so widespread when they added it as an option to the missal. But in the intervening years since the Council, the majority spoke and it became so. Thankfully in this day and age, there are still some of us who prefer the priest to turn toward the East along with the rest of us when offering the sacrifice.