Koichiko separated from Koichi and started going out with Viet.
We broke up due to a lack of communication.
When I parted from her, I couldn't stop crying.
Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means separate, so you can guess the meaning is to separate or to be divided.
Remember the word 分ける? That word means "to separate" too. The reading is similar, though not the same, but we can at least use it as a jumping off point. We go from わける to わかれる. It's like we've "separated" the け and the る and combined them in the middle. け, making a かれ, which gets you to わかれる.