米国のペンフレンドと文通し始めて１年になる。

。

It's been a year since I started exchanging letters with my American pen pal.

Literal

America's pen-friend [with-と] correspondence start [and-て] 1-year [to-に] become.

文通し始めて１年になる uses the elapsed-time pattern: ~て + duration + になる ('it has been [duration] since'). ペンフレンド is a loanword for 'pen pal.' 文通 means 'correspondence/exchanging letters.' The whole sentence captures a milestone.