The speaker promises her everything her heart could ever desire. I have copied the poem here, and my analysis appears in brackets every few lines as necessary.

Come live with me and be my love,
And we will all the pleasures prove

(He promises her "all the pleasures" not only be promised, but realized, "proved".)

That valleys, groves, hills, and fields,
Woods, or steepy mountain yields.
And we will sit upon rocks,
Seeing the shepherds feed their flocks,

(They will live a life of ease, watching others work while they lounge.)

By shallow rivers to whose falls
Melodious birds sing madrigals.

(They will enjoy all the beauty and pleasure nature has to offer, in peace and tranquility.)

And I will make thee beds of roses
And a thousand fragrant poises,
A cap of flowers, and a kirtle
Embroidered all with leaves of myrtle;

(More pastoral pleasures; a life of ease infused with natural beauty that delights all the senses. The last line in here also gives the beloved reason to not worry about things like how the pair will clothe themselves or have money for other things. Nature, and their love, will be enough.)

A gown made of the finest wool
Which from our pretty lambs we pull;
Fair lined slippers for the cold,
With buckles of the purest gold;

A belt of straw and ivy buds,
With coral clasps and amber studs;
And if these pleasures may thee move,
Come live with me, and be my love.

(Not only will they be cared for, but they will be arrayed in the finest things.)

The shepherd's swains shall dance and sing
For thy delight each May morning:
If these delights thy mind may move,
Then live with me and be my love.

(How could she turn him down?? :)