Rest in soft peace, and, asked, say, "Here doth lie Ben Jonson his best piece of poetry,
The speaker tells his son to rest in peace.
Then he gives him some other advice, which is kind of hard to make out. The sequence of words "Ben Jonson his best piece of poetry" is slightly odd, we have to admit.
Here's the deal, though: the speaker tells his son that, if he (the son) is asked, he should tell folks that he (the son) is the "best piece" of Ben Jonson's poetry. (It's not clear who, exactly, would be asking the dead son questions. Angels? Other people in Heaven?)
Basically, the speaker wants his son to say "Here Ben Jonson has laid to rest his best piece of poetry." This is a pretty important metaphor, in which the speaker refers to his son as a work of art.
For whose sake, henceforth, all his vows be such As what he loves may never like too much."
The speaker concludes the poem by telling his son that he (the speaker) will make a vow.
The speaker's vow will be never to "like too much" the things he loves. In other words, if he loves something, he's not going to get too crazy about it because you never know when it will be taken away. Sad.
The structure of line 11 is a bit wacky. It could either be a command (the speaker is commanding all his vows to "be such") or a prediction (the speaker's vows will "be such").
In either case, it is clear by the end that the speaker is encouraging himself not to "like" the things he loves "too much." Can you relate to this, when you love something, but you also like it too much? It sounds weird, but the idea is that there is a price to pay for being too attached to something in this life. Again, it's not a very cheery thought, we have to admit.