How can i teach myself how to sing really good at home by myself?

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Sing, Don't Let Nobody Stop You

Listen to the radio or a tape of a favourite song. match your tones to that...But it is vital that you corectly adjust your singing to match a good singer. often we are our own worst critic or we give ourselves too much credit...So make a tape of your own voice and play the tape as well as the professionally made tape as well at the same time...dont be too hard oon your skills becasue they have professional mixers and musicians

Ok just sing a lot
a lot
a lot

but if you want to not just sound good in your head but sound good to others too then get basic lessons.
Its like math
you can't do calc. without knowing how to add
same with the voice
you must learn the basics before you start trying to sound like the pros
so invest in some lessons or just join a choir
They will teach you some basics that you can build on in your own free time trying to sound like the songson the radio!

sing loudly to broadway music or taylor swift. both have noticeable vibrato you should try to match and are fun to sing.

You can't. You can either sing or you can't sing and there is no teaching involved. You should know if you can do it. If you have to "learn," you can't so just skip it. You were either born with a singing voice or you weren't. Period!

record.yourself
playback
critique.yourself