1. want subject to invent: lack subject matter which will inspire the imagination.

3-4. Thine own sweet argument: An "argument" is a theme or subject; the poet's idea is that his beloved is the best possible theme or subject for a poem. | too excellent / For every vulgar paper to rehearse: i.e.too good to be the subject of ordinary popular poetry. "Vulgar" means "popular"; "paper" is a metonymy for "poetry"; and "rehearse" means "say over and over."

5-6. if aught in me / Worthy perusal stand against thy sight: if any of my writing that is worth reading come within your sight.

7. dumb: silent, uninspired.

8. thou thyself dost give invention light: i.e., you yourself teach the imagination what to say.

9. the tenth Muse: The Muses are the nine "goddesses who inspire the creation of literature and the arts" -- Wikipedia: Muse.

12. numbers: verses. long date: a great span of time.

13. curious: critical.

14. pain: effort, labor.