“As a kid, my dad was taught to take the Eucharist in his mouth, but now you can take it on your tongue or in your hands. Which is correct?”

The old saying "The more things change, the more they stay the same" certainly applies to the Catholic Church.
I'm not sure how old your father is, but he's not alone in recognizing the many changes of the past forty years. For example, long ago most people received Communion only once in their lives, so the Church made a regulation for Catholics to go to Communion at least once a year. Called the "Easter duty," it was to be preceded by going to the sacrament of penance.
During some periods in history, Catholic teaching emphasized the divinity of Christ, and his humanity was not given equal weight.
One consequence was that many people felt unworthy to touch the Eucharist with their hands. However, over the past seventy years scholars have discovered evidence that the early Christians received the Eucharist by putting their hands together to make a "throne" in which the Lord was placed.
In the years since the Second Vatican Council, this practice has grown in the United States.
Both ways of receiving the Eucharist are permissible, so it isn't important which you choose. What is important is that you receive it with reverence and believe that as you receive it, you witness your faith in Jesus' life, death, and resurrection.