Letter writing is one of the under-utilized methods by left-wing groups. It has an extremely good track record. Politicians
care what registered voters in their district think. Also, hand written submissions have in the past been seen as more effective than boilerplate letters or emails. The trick is to convince the politician of the authenticity of the sentiment.
Petitions are basically worthless from what I've heard. Signing a petition is probably the least useful thing you can do.
Public protests have mixed results, but can be easily manipulated to turn public opinion against the protestors. A public protest isn't going to get your message out to the public unless the media is already
sympathetic to that message. YMMV but disruptive protests by groups who aren't in favor by mainstream media aren't going to achieve your goal.
A lot of the "Socialist revolutionary" (SR) type groups who hand out lefty papers - who achieve fuck all basically - focus on the
least effective methods, e.g. disruptive protests. My theory is that those sort of efforts thrive not because they're effective at causing political change, but because they're effective in perpetuating the group infrastructure that organizes the protests. And the us/them dichotomy created by the backlash to protests perpetuates an "in-group" mentality which maintains the group identity.
Weirdly, the SR types agree that incremental law changes can make things
worse but they'll argue till they're blue in the face that no incremental law change can make things
better. Which is a contradictory worldview for obvious reason.
Notably, the PR firms behind mega-corporations co-opted the tactics of left-wing activists in the 1960s, to create "astro-turf" organizations, and I'd suggest the Tea Party is an extension of that. If you want to know what works, go look at what Astro Turf groups do and steal the tactics back. Basically the astro-turf PR firms have distilled down how to influence politicians for you, go learn from them