If you want to talk to your mother in Japanese, call her おかあさん. This is like calling your mother "mother". Small kids sometimes call their mother ママ ("mommy"), but since you're probably older than 10, you should stick to おかあさん. (And no, it's not too formal. Anime Japanese is not really known for being too formal...)
There are cutefied or colloquial variants on おかあさん, like おかあちゃん, かあちゃん, かあさん.
By the way, it's also possible to talk about your own mother using おかあさん, as in うちのお母さんが…
Just to be clear, 母 is not a form of address, but expresses the biological relationship "mother". Talking to your mother, you wouldn't address her with 母. You can use 母 in principle for talking about other mothers (太郎君の母を見ました), but this sound like "I saw Taro's biological mother".
In the olden days, 母上 was (and in Samurai circles still is) a formal way of addressing (and talking about) your own mother.