It's difficult for us, too, and I think it's advanced Japanese when it's read あま and あめ. Generally they are used for the phrases from old Japanese language. Now, in everyday conversation, we rarely use あま and あめ. I think there are rules but they aren't very clear. So one of the best ways would be remembering how to read it in each case. I hope this helps you.

It is easy to see the difference between テン (ten) and 天 (heaven, sky) when you're reading or if you want to write it. The katakana word テン can only mean "number ten" from english and the kanji 天 is heaven or sky (there are some other meanings) , but on conversations, the context will be crucial. あめ and あま are different words with different meanings. あま could mean "nun" and あめ most of the time means "rain".