The underlying principle
The indicativo presents something as a fact, as knowledge or observation. The subjuntivo presents it through a subjective filter: a wish, a doubt, a feeling or a judgement. What matters is not whether something is objectively true, but how the speaker frames it.
The core contrast
Creo que viene mañana.
I think he is coming tomorrow. (fairly sure)
No creo que venga mañana.
I do not think he is coming tomorrow. (I doubt it)
The triggers in front of que
Indicativo — fact and certainty
Sé que está aquí.
I know he is here.
Es verdad que trabaja mucho.
It is true that he works a lot.
Subjuntivo — wish, doubt, feeling, judgement
Dudo que tenga razón.
I doubt he is right.
Es importante que trabajes mucho.
It is important that you work hard.
Negation flips the mood
Negate an opinion and its content stops being a claim and becomes a supposition, so the mood moves from the indicativo into the subjuntivo.
English hides this rule. I think he is coming and I do not think he is coming use the very same verb form, coming; only the little word not moves. Spanish reacts to that not by rebuilding the verb.
Me parece que es buena idea.
It seems to me that it is a good idea.
No me parece que sea buena idea.
It does not seem to me that it is a good idea.
Quizás and tal vez
After quizás and tal vez (maybe) both moods are possible. You choose by how sure you are: indicativo sounds more confident, subjuntivo more doubtful.
Quizás viene hoy.
Maybe he is coming today. (fairly sure)
Quizás venga hoy.
Maybe he is coming today. (rather doubtful)
Hear the mood change
trabaja
he works — indicativo
trabaje
(that) he work — subjuntivo
come
he eats — indicativo
coma
(that) he eat — subjuntivo
está
he is — indicativo
esté
(that) he be — subjuntivo
