First of all, there is practice, and practice and practice.
Secondly there is practice. Do you drive to work, alone? Practice. Need help? put a CD on the player. Need more help? learn the words, word perfect. Never let the singing falter in order to find the words.
Then a bit of practice might help.
Singing in a choir, or at a Folk Club with the chorus. I always recommend shanties because they are work songs and gruff works with them. Rhythm is everything there. Tune? Act the hauling and tunes will vanish anyway. You are acting a part, even if the singing is only a part.

Now it is a fact I rejoice in telling that I never sang till the wife left home. & I daren't stop in case the magic wears off. Motivation helps a lot, you see. Find the right reason to sing, and find the right tunes. It is no good singing meaningful lyrics to a slow air if you are not fully confident - shanties I tell you, & comic songs. The meaning in those lyrics is not carried by the tune - the rhythm probably, the rhyme definitely. Find the easy routes first.