"I do not go to school on Sunday."
Translation:No voy a la escuela el domingo.
It seems to be just a general rule that when you are referring to days of the week you use the article in front of it instead of a, en, or de. For example I attend yoga classes on Sundays would be "asisto a yoga los sabados". If it's in general, like all the Sundays, you use the plural, and if it's on a specific one you use the singular.
I don't know if this helps, but knowing the origins of the names of the week in both languages helps. Saturday is literally "Saturn's day" and "sábado" sounds a little bit (to my ears) like the word "Saturn" - although as above, it is based on the word "sabbath" which is, of course, Saturday.
Check out this fascinating explanation of the origins of the names of the week.
P.S. I remember viernes=Friday because Venus and Fria are the only two female gods in the names of the week in both languages.
Sunday Sun: Domingo Dominus (Lord); Monday Moon: Lunes (Moon); Tuesday Tiw (heroic glory) : Martes (Mars: war); Wednesday Odin (poetry): Miercoles (Mars: poetry); Thursday Thor (thunder): Jueves (Jove: thunder); Friday Frigga (Thor's wife): Viernes (Venus: Love); Saturday Saturn (agriculture): Sabado (Sabbath)
Sabbath originally referred to Saturday. Sabbath still means Saturday for some people, mainly those of the Jewish faith.
The way I learned the Spanish day names was to memorize it as a whole list the way a kid would.
Say the list 10 times every day for 10 days (really)
lunes martes miércoles jueves viernes sábado domingo
Saturday is the Sabbath (the day of rest), even in Christianity. Sunday is "the Lord's day", which is more important to most Christians. You can remember that factoid by thinking of Good Friday and Easter Sunday. In between, there was a Sabbath, when Jesus rested.
If you think of Sunday as "the Lord's day", this will help as well, since "domingo" is related to the idea of "dominion", something a lord has.
Regarding "la escuela," there are several answers that all seem to variants of "because that's how it's done in Spanish." That's fine, but if you need the definite article for a generic reference, what do you do when you need a specific reference. Imagine a maintenance worker that visits several public buildings.
"I don't go to the school on Monday. I go to the hospital. On Tuesday, I go to the school."
It seems that would be the same translation: No voy a la escuela.
Is it only context that allows us to parse the sentences correctly?
I realize you posed this question a couple of years ago, but I'll answer it in case it helps others with the same question.
For the most part, yes it is context, but you can also use a demonstrative pronoun to indicate you're talking about a specific place. In other words, your sentences could be:
«No voy a ésa/aquélla escuela el lunes. Voy al hospital. El martes, voy a la escuela.»
Notice how the inclusion of the demonstrative pronoun in the first sentence sets the stage for the other sentences so it is clear from context that you are referring to the specific locations.
When two vowels are together in most languages there is often a way to modify it so you don't have to clumsily pronounce them. In English we change "a" to "an" to avoid this mixing of vowel sounds. In French they combine vowel sounds as well, for example, le + homme=l'homme.