I disagree
A softer, more personal way to disagree, literally 'I don't think the same.'
A very common and slightly indirect way to say 'I don't think so.'
A more direct way to disagree with a fact, meaning 'That's not true.'
A polite way to frame your disagreement as a personal viewpoint, meaning 'In my opinion, no.'
He says blue is the best color, but I disagree.
—This city is boring. —I don't think the same, I love it.
The bus arrives at five? I don't think so, I think it arrives at six.
They say it's going to rain, but the sky is clear. In my opinion, no.
'No estoy de acuerdo' is the standard, universally understood phrase across all Spanish-speaking countries.
'No creo' (I don't believe so) and 'Yo digo que no' (I say no) are very common, slightly more informal ways to express disagreement in conversation.
The phrase is the same. You might also hear 'No comparto tu opinión' (I don't share your opinion) in more formal or polite situations.
While 'No estoy de acuerdo' is perfectly common, you will frequently hear 'Para mí, no' (For me, no) or 'Me parece que no' (It seems to me that no) to soften the disagreement.
The standard phrase is most common. In casual contexts, people might say '¿En serio? A mí no me parece' (Really? It doesn't seem so to me).
Saying 'Yo no acuerdo'. — The verb 'acordar' by itself means 'to agree on something' or 'to decide', like in 'Acordamos vernos mañana' (We agreed to meet tomorrow). To express the state of being in agreement, you must use the full phrase 'estar de acuerdo'.
Using 'disacuerdo' as a verb, like 'Yo disacuerdo'. — 'Disacuerdo' is not a verb in Spanish. It's a noun meaning 'disagreement' ('Hay un disacuerdo'). The correct way to say 'I disagree' is 'No estoy de acuerdo'.
Using 'No' by itself in a polite context. — Just saying 'No' can sound too direct or even rude, depending on your tone and the situation. It's often better to use a full phrase like 'No estoy de acuerdo' or 'Yo creo que no' to be more polite.