It's unlikely that you will learn the verb "tatschen" early on in any German class if you're an English native speaker. Why?
It is too easy to remember.
The pronunciation of "tatsch" and "touch" is basically indiscernible, and "tatschen" does in fact mean "to touch". But - and here's the kicker - it means touching in an inappropriate manner. That makes "tatschen" and "touch" two of the most vicious false friends in existence.
"Tatschen" is typically combined with the prefixes "be-" and "an-" and may refer to harmless scenarios, such as not wanting somebody to touch certain objects: "Ich will nicht, dass die Kinder meine Porzellansammlung antatschen." (I don't want the kids to antatschen my porcelain collection.) It may however also refer to sexual harassment: "Der gruselige Typ im Bus hat versucht, mich zu betatschen." (The scary guy tried to betatschen me on the bus.)
Thus, unless you specifically refer to the kind of touch that is unwanted, you should use the words "anfassen" or "berühren" when speaking German.