I can go up to the roof.
I climbed up stairs to the 10th floor.
I saw a salmon swimming upstream.
This vocab word is an exception in almost every way. It has a similar meaning to the meaning of the kanji, and you know it's a verb because it ends with an う sound (る, in this case). But, the meaning is to climb. Comparing it to the other 上 verb words, it has the least okurigana (versus 上げる and 上がる). You could remember this and know that the thing you don't want to do the most is "to climb," so that's why it has the least okurigana.
The reading for this word is an exception from all the rules of the 上 vocabulary. It consists of a kanji with hiragana attached, so it will use the kun'yomi reading. You didn't learn that reading with this kanji, so here's a mnemonic to help you: You want to climb the mountain, but a gruff old man grabs your shoulder and says "No boy, you ain't climbing that thing, not today." If you're not a boy, think about how weird it is that he called you a boy. If you are a grown man, think how you wish he called you "dude" or something, not "boy." If you're a boy, well... think about how appropriate it is that he said "no boy."