No real fast way honestly, I suggest you download the Tenuto app and practice in the chord section as much as you can. There’s a website version too. Good luck

I decompose mentally, and then reorder also mentally to find the root note and the basic chord, then sing again mentally again to see in which position the bass note is compared to the root note. The best is to just read scores of music you like, sing mentally all the notes vertically, simplify to the just 2 (a lot of chords have 5th removed in Mozart/Haydn music, it's more elegant with just 2 notes! ) or 3 or 4 or more notes of the chord, so it become a pleasure instead of an exercise. First time it takes you 1 minute for 1 accord (or more), and then it becomes nearly instant

Hey, Jasmine! My favorite way is to have a melody/song association for the interval- For example:
For m3 and M3, you can sing them and hear that they're the beginning of a Major or minor chord.
For P4- Here Comes the Bride or the beginning or Old McDonald Had a Farm
P5- Twinkle Twinkle Little Star
Etc. Maybe that can help!