“how thy worth with manners may I sing”
'With manners' means decorously, with proper social propriety. The problem the poet identifies is that praising the youth is a form of self-praise, which good manners forbid: since 'thou art all the better part of me,' any compliment to the youth reflects back on the poet himself, making praise tactless rather than generous.
historical The sonnet form“let us divided live, And our dear love lose name of single one”
This is the sonnet's central conceit: the poet proposes that he and the youth live apart so that he can praise the youth without praising himself. If they 'lose name of single one' — stop being counted as one person — separation creates the distance that makes genuine tribute possible. The argument is paradoxical: love is best served by the appearance of division.
historical The sonnet form“how to make one twain, By praising him here who doth hence remain”
'Twain' is an archaic word for 'two.' The couplet clinches the sonnet's paradox: absence teaches the poet 'how to make one twain' — how to turn what is essentially one person (the youth as the poet's better self) into two distinct figures. It does so through the act of writing: by praising 'him here' (present on the page, in the poem) who 'doth hence remain' (physically absent, departed from here), the poet creates the very distance that genuine praise requires.
historical The sonnet form