The delicious curry was finished.
Our Japan travel plans were finished at the last minute.
The tofu and fugu hamburgers are done!
You've seen the word 出来る (to be able to do), which is the first part. Then the second part, 上がる means "to rise." So, think about it this way: once you're able to do something, you rise because you're finished. That's why this verb means to be finished.
The reading is a combination of the readings from 出来る and 上がる. So long as you were paying attention in lessons past, you should be able to read this word as well just by combining those other words.