Although I've been a member of the two local groups that I belong to for oh, about 20 years now, it wasn't until this year that I realized (D'OH!!) that the Taxi forum IS A SONGWRITING GROUP!!! That said, while on-line might be the new 'next best thing to being there', there's nothing like live and in person.
Obviously, it's easier to join something that's already established. The Nashville Songwriters Association International (NSAI; http://www.nashvillesongwriters.com) has local groups all over the world, and provides a ton of benefits to it's members. The Songwriters Guild of America (http://www.songwritersguild.com) is another. The NSAI website allows you to search for chapters, and the SGA offers regional events in NYC, Nashville and LA. There are many other songwriting groups (Baltimore Songwriters Association, Connecticut Songwriters Associateion, etc.), so a google search is a good place to start. For example, the Philadelphia Area Songwriters Alliance (PASA) is about 45 minutes from me, has a website and regular song-circle meetings, bi-annual workshops, and semi-open mic house concerts...
The first songwriting group I joined was a "Producers and Songwriters Guild" group initially formed by two local songwriters, Ruth Wyand and Tony Deluca. Unfortunately, both were also professional gigging musicians and after about a year of (mostly) cancelled meetings (since they were usually working), the group folded. Ruth, Tony and I re-formed it the following year as the Garden State Songwriters, and it's been active (in one form or another) ever since. Currently, there are only a few regular members, as many occasional members, and we only meet once a month, but it's something.
The late Jack Hardy (d.2011) ran a songwriting group in NYC for years, and fostered the careers of a veritable 'who's who' of contemporary folk artists like Suzanne Vega, Shawn Colvin, John Gorka and others. I've looked online for his manifesto, and although I haven't been able to find an exact copy, the principles of the meeting are simple, but challenging:
1) Write a song a week
2) Meet with other songwriters every week
3) Bring some good food or drink to share (potluck!)
4) Play your new song (unfinished is ok) for your peers (only people with a NEW song get to play)
5) Focus on what is being done RIGHT in the songs you hear and give positive feedback (tell what you like about it... if you can't say something nice...

6) Get over yourself; leave the ego at the door... it's all about the song, silly!
If you can't find an already established local group to join, you'll have to start your own. Start by deciding on a place and time to meet. Since it's your group, meeting at your house is the most natural place. If that isn't feasible (for whatever reason), and you don't know anyone willing to volunteer their house, you'll have to look for something a bit more public. Bookstores, coffee houses, restaurants, church basements and public libraries are all possible venues, each with their own unique pros/cons, but you need some place regular. (Scott Hanson, you could do host at your restaurant...

As far as when, I recommend Monday or Tuesday nights; these are the least likely nights for band members to be gigging. If you can do it every week, great! That will really keep you writing, and will fuel great stuff. If not, at least make it a regular thing. (My GSS group met twice a month for a couple of years, and I was also going to the local NSAI meeting once a month, so I had at least three songwriting groups a month for awhile.)
Invite any songwriters you know to the first meeting. If you don't know enough songwriters, go to your local music stores and post something on the bulletin boards, and go to a few open mic nights. You'll find them. Or they'll find you. If it's at your house, put on a big pot of pasta and sauce and open a jug of inexpensive wine, and ask everyone to bring something good to share...
Break bread, share your songs, listen appreciately, and give positive support. Repeat.
Do that for a few years, and your songwriting is bound to improve. Good luck!