I don't know what level you're at but in general...
Start with diatonic (within the key). There are only seven notes that way.
Sight-sing from the music you see. Write down/dictate the music you hear. Try it on your own first and then go back and make corrections. I'm assuming you're working through an ear training book.
Just keep adding. Those books focus on one note like beginning piano method books do. Learn one note and add another.
Learning some patterns can help. 13531. 12345 54321 5671 You can make your own or borrow them from music. Or use snippets from stuff you mess up on. Just run through those each day to engrain them.
Practice getting that first pitch. Establish a key (V I). Then hit a random note in that key. Learn to tell what it is. Sometimes working with a partner can help on things like that, picking random notes. You can hit the keys with a pencil. Make a short recording and mix up the tracks (give yourself the answer at the end of the track).
You probably already know some without having to use a piano to double check. Or do some more practice on each topic so you don't have to check with the piano -- Why check if you already know what it is after awhile?
For chords, for singing them at least, you can only sing in arpeggios. 135 351 513 But you can break them up into inversions like that. Or use patterns again, 1531531. Alberti, etc.
Littletune asked similar questions awhile ago. She got some good replies.
Tests are another situation. It's a test. For me, my goal was to pass the test. It's kind of artifical. You can do things like very, very quietly air whistle to yourself -- There's a point where it's hard to tell if you're actually making noise or imagining it. If it doesn't bother anyone else and the instructor doesn't mind, that can be an option. It's really just thinking in sound. Actually air whistling is a temporary crutch.
I learned with movable do. For awhile it was a little extra mental effort to figure out what step was what solfege, but knowing the major and minor scales already helps a lot for that.