は and が: topic and focus
A fixed one-to-one translation of は and が misses important context. Ask what the conversation is about and which information the speaker is identifying or highlighting.
Set a topic with は
私は学生です。 means 'I am a student,' with the speaker as the topic. As a particle, は is pronounced wa. A topic can coincide with the grammatical subject, but the two are not always identical.
In この本は読みました。 ('I have read this book'), the object being read is the topic. Do not assume that the phrase before は always identifies the person performing the action.
Identify the subject with が
Answering 誰が行きますか。 with 私が行きます。 identifies who will go: 'Who is going?' — 'I am.' The focus is on supplying the person missing from the question.
が also appears when reporting a situation, as in 雨が降っています。 ('It is raining'). However, a rule based only on mentioning something for the first or second time cannot explain every sentence.
Read contrast in context
コーヒーは飲みますが、お酒は飲みません。 means 'I drink coffee, but I do not drink alcohol.' The two instances of は establish a contrast between the objects, not just information about the act of drinking.
Practice with a preceding question rather than only a gap in an isolated sentence. Distinguishing an explanation about a topic from identifying a particular person makes it easier to explain your particle choice.
Check: To identify yourself in answer to 'Who is going?', is 私は or 私が more natural?
Show the answer and why
私が行きます。 is natural here because が answers the question of who is going. This does not mean that 私は is incorrect in every context.