How do you stay on your note and know that you are singing the right note?
Not everyone hears in the same way. Many people “feel” sound more accurately than they hear it at first. Eventually, they learn to connect what they are feeling with what they are hearing and can develop correct pitch and tonal memory. Sometimes you can know that you are singing the right note because it seems like your voice disappears into the sound of the pitch you are to match.
Sometimes the inability to stay on pitch is a technical issue, such as a lack of adequate breath support or a lack of overtone in the resonance.
You will need to work with someone who has experience and loves helping people learn to match pitch. Not all teachers are strong in this area.