What does this saying by Shakespeare mean? When daffodils begin to peer... Why, then comes in the sweet o' the year... Good morrowHe used Old...

This is from the song that opens Act 4, scene 3 of
The Winter's Tale.  The rogue Autolycus is singing about how, as
the first response noted, it is springtime, the sweetest time of the year, during
which he can chase after women, engage in thievery, and drink
ale. 

Also, Shakespeare did not write in Old English.  If
you take a look at the poem Beowulf in the original, that is Old
English.  Grab a copy of Chaucer's Canterbury Tales in the original
to see what Middle English looks like.  Shakespeare is actually modern English, although
the spelling of various words has changed over time.  What you see when you grab a
modern edition at the library or bookstore is something that has been edited: the
spelling cleaned up, the punctuation regularized, etc.  But it is still modern English. 
With practice and some good footnotes to help with the obscure words, Shakespeare needs
to no translation (at least not like Beowulf
does).