carefully, gently
neatly
He laid the clothes neatly on his bed.

aside, down
With a resigned sigh she laid aside her book.
He laid the plates down on the table.

on
She laid the child tenderly on the bed.

over
They carefully laid a blanket over the body.

nicely, well
Each chapter is nicely laid out with clear diagrams.

clearly
The information is there; it just isn't laid out clearly.

Lay is used with these nouns as the object:
ambush, blame, brick, cable, carpet, charge, claim, concrete, drain, egg, emphasis, foundation, groundwork, hand, head, kiss, main, mat, mine, odds, palm, pipe, pipeline, place, responsibility, siege, stress, table, tile, track, trail, trap, turf, wreath

Lay is used with these nouns:
audience, ministry, preacher, reader