わたしはえいごをべんきょうします。(When I hear this sentence without any context, what I imagine is "I'll study English".)
わたしはえいごをべんきょうしています。(It means "I'm studying English now" and "I study English habitually", "I'm in the situation that I study English / I already started studying English".)
With more context:
わたしはあしたがっこうへいきます。(I'll go to school tomorrow.)
わたしはまいにちがっこうへいきます。(I go to school everyday / I'll go to school everyday.)
わたしはまいにちがっこうへいっています。(I go to school everyday.)
わたしはバスでがっこうへいきます。(I go to school by bus / I'll go to school by bus.)
わたしはバスでがっこうへいっています。(I go to school by bus.)
If you need more examples, please let me know.
I hope this was helpful.