Chci se omluvit za nepřítomnost v hodině. I want to excuse for/ from my absence.
I want to apologise for my absence.

Co je prosím správně?

I want to excuse my absence
I want to excuse for my absence
I want to excuse from my absence

Jinak je oboje v pořádku.

I want to apologise for my absence.
Please excuse my absence.
I am sorry I didn't make it to our last meeting (or whatever)
I am sorry for not being at the meeting…

To apologise cítím jako silnější.

To “from” má jiné užití. To je když se omlouváte z něčeho
Tady posílám příklady z Camridge výkladového slovníku:
I asked the teacher if I could be excused from (= allowed not to do) hockey practice as my knee still hurt.
Please excuse me from (= allow me to miss) the rest of the meeting – I've just received a phone call that requires my immediate attention.

Dobrý den, Danieli, domnívám se, že ta vaše druhá věta je chybně. Nemám už teď ale čas to zkusit rozebrat.. Vrátím se k tomu odpoledne, až budu mít chvíli..

Eva is right. Sentence two “I want to excuse for my absence” isn't possible because excuse is transitive: the object has to be stated. At a pinch, you can say I want to excuse myself for my absence – see the Ngram. It will be understood but it sounds like foreign language interference here when it's used after the absence.

Excuse oneself (from) is used (if at all) before (not after) the absence occurs. It means I intend/plan/ex­pect/want to be absent from … The speaker is asking to be excused from something that hasn't happened yet.

Eva's first two versions are the most natural here. If the style is less formal, Eva's versions 3 and 4 are fine too.

Apologize, of course, is the AmE spelling.

See also Jak se omlouvat v angličtině.