Start writing. If you are not an experienced poetry writer, research some famous poets, such as Robert Frost or Edgar Allan Poe, so that you can come up with a writing strategy of your own. Probably the best known love sonnets are Shakespeare's. Check them out. He knew how to turn a phrase and how to express love in interesting and unique ways.
A love sonnet can be loaded with emotion, so let the sentiment flow. Just as Shakespeare knew how to fill a sonnet with emotion, you can seek out new and interesting ways to express love. Trite poetry is poor poetry. Good sonnets are fresh, fun to read and offer the reader interesting insights.
Make sure to edit well, or have someone else edit well for you. Any imperfection or error in grammar, spelling, etc. will lead to getting rejected by a publication that might otherwise have been interested.
Look for a place to publish your love sonnet, online or off. Look up local magazines, newsletters, newspapers, to see who publishes poetry in your area. Also, there are many websites that publish poetry for free, such as poetry.com. Submit your work and hope it gets accepted.
If your work does get accepted and if whoever accepts it is entitled to exclusive rights to your sonnet, make sure you notify anyone else you submitted to that your piece is no longer available.