Drink to me only with thine eyes,
And I will pledge with mine;
Or leave a kiss but in the cup,
And I'll not look for wine.
The first stanza establishes drink as a metaphor for love.  It opens with an imperative; the speaker wants the woman to focus her feelings through her eyes.  This follows an age-old concept of the eyes being the means to project emotions, a wordless language. Here, their gazes to each other are so intoxicating that they do not need alcohol. 
 The word ‘only’ is ambiguous.  It could mean ‘drink only to me and no-one else’ or ‘it is only eyes that should be means to convey emotions, not words or actions.’  Both apply.
Song To Celia