Don't forget, Echo is talking (or singing) to a fountain, so water is a Big Deal in this one. In fact, the scene in the play from which "Slow, Slow, Fresh Fount" comes takes place near a body of water, and Echo, the speaker of the poem, waxes poetic on water several times in the poem. In addition to the "gentle springs" and the "fresh fount" of the title and first line, Echo also mentions her "salt tears," and "melting snow." And in every case, she makes a strong association between water and sadness, suggesting that the soggy stuff just might be a symbol of her grief.
Line 1: Echo tells the "fount" to "keep time" with her "salt tears." Both the tears and the fount are symbols of sadness or mourning. A "fount" isn't a person and can't really "keep time," so this is an example of personification, the attribution of human qualities to a non-human object. The repetition of the first letters of the words "slow" and "salt," and "fresh fount" is called alliteration, and it helps give the first line of the poem a sad, slow tone.
Line 2: Echo tells the "gentle springs" to keep time more "slowly." And again she's using personification (gentle springs can't actually keep time) and alliteration ("slower" and "springs ").
Line 6: The speaker tells grief to "fall in showers." She could either be referring to her tears and mean something like "my grief, show yourself by falling in showers," or she could be asking nature to show its grief by raining. Either way, these showers are sad business.
Line 9: Echo compares herself to "melting snow" in a sorrowful simile. But Jonson packs a one-two punch into this line because the "melting snow" is also a metaphor for both death and grief, which is a slow, slow process.