The heavens declare the glory of God; literally, the heavens are recounting the glory of God—of El, "the Mighty One"—the God of nature (see Romans 1:20). David is perhaps carrying out his declared intention (Psalms 18:49) of praising God among the heathen," and therefore takes their standpoint—the ground of nature.
And the firmament showeth his handywork. (On "the firmament," see Genesis 1:6, Genesis 1:20.) It is the entire atmosphere enveloping the earth, in which the clouds hang and the birds move. Like the starry heavens above, this, too, "showeth," or rather, "proclaimeth," God's handiwork.