Are all the best efforts truly local, or are there good regional/national causes (for example, the Rails-to-Trails Conservancy) that are worth supporting?
The best form of advocacy is to ride as much as you can. In the developed world we tend to look at cycling as recreation or a hobby. As such, many participants drive their bike to the place where they ride their bikes.
The more visible you are to your friends, neighbors and co-workers as a cyclist, the better. The more you ride for transportation, or utility the more 'credibility' you have with those around you.
Begin in your local community. If you ride to the store, restaurant, or library and there is not a convenient place to lock your bike, talk to the manager. On a couple of occasions I have mentioned to a manager that I and other cyclists like a particular restaurant but we don't visit as often because there is nowhere to lock our bikes other than a chain link fence, or a tree. Two 'strip malls' now have bike racks.
Finally, your town or county may have an advocacy group already - join - be active.
Showing example is a great way for cycling advocacy.
People around me take usage of car for granted. But when they see me riding my bike everyday for working, for shopping or just for the pleasure of cycling, they start to question their behaviour. There is still a long way before they are converted but the seed has been injected in their mind.
There are lots of cycling clubs that are associated with IMBA (International Mountain Biking Association). These clubs often run events and maintain trails.
By joining an IMBA club, you'll help support efforts on a regional and national level.
One of the aspects of Cycling Advocacy is to make cycling more popular. My usual approach to this is to get work colleagues to volunteer to take part in a charity bike ride a few months from now (we usually do the Manchester to Blackpool Bike Ride in aid of The Christie which is about 60 miles long).
Out of the various people who volunteer and do the bike ride each year, a number carry on cycling (if they hadn't already been keen cyclists), this was what got me back into cycling a few years ago, now.
So my suggestion would be to try and get friends or colleagues to do something cycling related with a few months to prepare for it, and hope that as a result they will rediscover cycling and become once more converted to the Way of the Bike.
Adventure Cycling Association is a great group. Their nonprofit mission: "to inspire people of all ages to travel by bicycle for fitness, fun, and self-discovery."
Although there are great local groups, some things are best addressed by nationwide efforts. The vote in the US Senate over transportation funding - MAP-21 - was publicized and lobbied over by groups like the League of American Cyclists - and I think that was instrumental in getting things changed for the better.
This question has answers which include organizations all around the world.