Learn Arabic (Modern Standard): اليوم الأحد.

In Arabic, simple present tense sentences don't use a verb for "is" or "are". You simply put the subject, اليوم, and the information about it, الأحد, side by side to create the meaning.

Normally, the second word in an "is" sentence is indefinite and doesn't have "al-". Why do both words start with ال here?

You are right that usually the pattern is a definite subject plus an indefinite description. However, because days of the week in Arabic are specific proper nouns, they inherently take the definite article ال. So the sentence literally structure acts like "The today is the Sunday."

Does the word الأحد have a connection to the number one?

Yes! Most days of the week in Arabic are based on numbers. الأحد shares the same root as the word for one, واحد, because Sunday is traditionally the first day of the week in the Arab world.

Why does اليوم mean "today" when it just looks like the word for "the day"?

While the base word يوم means a day in general, adding the definite article to make it اليوم is the standard way to say "today" in Arabic, referring specifically to this current day.