How to Chant the Psalms
The backbone of chanting the hours is the Gregorian psalm tones.
There are 8 main Gregorian modes with a few more. CC watershead has excellent recording of what they sound like. Here is the page listing them: https://www.ccwatershed.org/2023/11/29/pdf-download-eight-gregorian-psalm-tones-harmonies-by-jeff-ostrowski/
The mode you use is determined by the antiphon you say. There are multiple sources for antiphons in Latin in the OF. The antiphonale Romanum 1 and 2 contain the antiphons for lauds and vespers for Sundays and solemnities. The ordo cantus officii which someone graciously transcribed contains antiphons for throughout the year https://www.reddit.com/r/divineoffice/s/qu6s15Sl9j
For the English translation, there is no official set of antiphon tunes. The mundelein psalter is the only version that has music in it. That being said you can adapt the Latin melodies to the English text or just use the psalm tones for chanting the antiphons.
If you are starting out, I would recommend sticking with one psalm tone probably 2 or 8 for a week or two and chant the psalms and canticles with that and gradually build up.
Chants and rants the podcast also has some useful information on this topic: https://www.youtube.com/@chantsandrants/videos