Pronounce "round". To pronounce 日, hold the "r" sound, i.e. hold the position of your tongue when you pronounce the "r" in "round". Additionally add the intonation of 去声. To get a clear sound, you could let your mouth open a little bit.
In Pinyin like zi/zhi, ci/chi, si/shi ri, we use "i" to stand for continuation of the consonant in the front [although in mainland China we do not actually use words vowels and consonants when teaching pronunciation to kids]. So likely, for "zi, ci, si", try to hold the position of /dz/, /ts/, /s/, and vibrate your voice box while you are sending air out.