You can learn songwriting online. One of the most popular websites for this purpose is SongU. It's quite expensive, $75 for three months but you're sure to learn a lot. There are some live lessons every week with some great instructors, including Robin Frederick (who wrote two of my favorite books, Shortcuts to Hit Songwriting and Shortcuts to Songwriting for Film&TV). You can also listen to the lessons later if you are unable to attend. You hear the teachers talking and you can ask questions real-time. These classes are usually one hour long. Sometimes they have a series of lessons on the same topic and you might get some homework. The most useful part of this website is that you can have your songs reviewed by professionals.
You could also join TAXI, which is an independent A&R company. They don't offer lessons but you can pitch your songs to various label and TV/Film listings and they review your work. The screeners are all industry pros so their feedback is a great songwriting lesson in itself.
Since constructive feedback is so invaluable, you might consider John Braheny's services too. He is the writer of the great book The Craft and Business of Songwriting . He offers custom-critique and his prices are not too high.
At NSAI (Nashville Songwriters Association International) they also review songs for a fee. I've heard mixed opinions about them and I haven't tried their services.
Then there are the songwriting forums (scroll down for a list of forums) where you can get in touch with fellow songwriters. Some of these folks are professional songwriters so it's worth visiting these places once in a while.
If you would like to get instruction offline, you could go to songwriting seminars. They are not only great learning opportunities but also great for finding co-writers or mentors.
Beware of songwriting scams though. There are some websites that offer you songwriting instruction and a publishing contract if you do well. These are usually scams. If only it was that easy…
Songwriting lessons will not make you a Grammy winning professional overnight. However, they can really speed up the process of getting there. But there is no better way to learn than to write songs every day. You know the saying: "practice makes perfect". In songwriting, it's 100% true. If you get only a little better every day and your enjoy the process, you'll get to where you want to be in no time.