Rails-to-trails , LAB and others are all great groups who do a lot of good, but not necessarily in your area.
Like the saying goes, "Think globally, act locally".
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.
bicycles.stackexchange.com/users/213/Gary.Ray
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.
bicycles.stackexchange.com/users/183/mouviciel
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.
bicycles.stackexchange.com/users/153/Dana the Sane
Buying from your local bike store that does advocacy, instead of ordering online or buying from Walmart.
bicycles.stackexchange.com/users/389/LanceH
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.
bicycles.stackexchange.com/users/79/Amos
Slightly silly but... public transport strikes.
Preferably in sunny weather!
bicycles.stackexchange.com/users/69/Murph
Here is a great link from Bikes Belong on effective methods of bicycling advocacy by individuals!
To summarize:
Ride your bike and represent bicycling Connect with local advocacy Connect/network with government and community leaders
Get involved at the national level
bicycles.stackexchange.com/users/None/
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."
bicycles.stackexchange.com/users/52/Rebekah
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.
bicycles.stackexchange.com/users/3644/Eyal
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?
What are the most effective methods of bicycling advocacy?
bicycles.stackexchange.com
<advocacy><resource>
bicycles.stackexchange.com/questions/856
bicycles.stackexchange.com/users/273/Mr. Palomar
The best way to advocate cycling is to ride a bike as much as possible. Some places have local cycling advocacy groups and it is also possible to become involved in these at national level. Encouraging friends and relatives to do something bicycle related is another good way of advocating cycling. One of the best forms of advocacy is to set an example and ride as much as you can, with the aim to normalize cycling and familiarize your local community with it. Another good idea would be to get organized on a regional or national level. To this end, you could join relevant groups or clubs, participate in transport strikes and get in touch with state representatives. You might also want to organize cycling activities for your friends, family and colleagues to make cycling popular with a broader audience. Finally, you could try supporting smaller regional stores against big chains.
One of the best forms of advocacy is to set an example and ride as much as you can, with the aim to normalize cycling and familiarize your local community with it. A good idea would be to get organized on a regional or national level. To this end, you could join relevant groups or clubs, participate in transport strikes and get in touch with state representatives. You could try supporting smaller regional stores against big chains. You might want to organize cycling activities for your friends, family and colleagues to make cycling popular with a broader audience.