上がる and 上げる: rise or raise positions and values
Compare upward movement with changes in temperature, price, and volume. Also distinguish を marking a route from を marking something that is raised.
Move upward or raise an object
Use 上がる when a person moves upward. 階段を上がって二階へ行きました。 marks 階段 with を as the route traveled, rather than as a direct object.
Use 上げる to move an object to a higher position. 重い箱を棚の上に上げました。 marks the box being moved with を and its destination with 棚の上に.
Changes in temperature, price, and volume
A value that rises takes が with 上がる. 午後は気温が三度上がりました。 says that the temperature rose by three degrees in the afternoon.
The value being raised takes を with 上げる. 音が小さかったので、テレビの音量を上げました。 marks the adjusted setting with を. The subject causing the increase does not have to be a person.
Everyday meanings selected by the noun
答えが分かった人は、静かに手を上げてください。 uses 上げる for raising a hand. お風呂から上がったら、髪を乾かしてください。 uses 上がる for finishing a bath and getting out.
雨が上がりました。 is an established expression meaning that the rain stopped. Do not force every sense of 上がる into a pair with something that someone 上げる; check the noun and actual meaning.
Quick check: How do you describe the result of the volume increasing and the action of raising the television volume?
Show the answer and why
For the result, say 音量が上がりました。 For the adjustment, say テレビの音量を上げました。 A changing value takes が, while an adjusted setting takes を.