We want to be very careful never to assume that the author of a poem is the same thing as the speaker – meaning that Elizabeth Barrett Browning, the Victorian poet you're studying here, isn't the same as the "I" who asks "How do I love thee?" Still, the fact that Barrett Browning wrote this sonnet for her husband, Robert, leads us to believe that the speaker of the poem is best interpreted as female, while the beloved is best interpreted as male. However, the way the poem is written leaves the gender of both parties in the relationship completely ambiguous. That's part of what makes it such a great love poem for the ages – anybody can send it to anyone else, without even changing a word. That gives you some idea of how undefined the character of this speaker is.
The speaker here, like the speaker in most sonnets, is a shadowy and uncertain figure. We don't know any concrete character details about her. But there are two things we're pretty sure of: she really loves someone, and she's really interested in listing and describing all the different kinds of love she feels for him. We also get the sense that she has a very complex internal emotional landscape; she loves someone intensely, but she also has "old griefs" – things she's bitter about – and "lost saints" – people she's lost her faith in and feels disillusioned about. She also talks about her "childhood's faith" as though it was in the far distant past, which suggests that this is a mature, older speaker, not a young girl experiencing her first crush.