Promote the petitions you support:

Send emails to your friends asking them to sign the petition.
Post links on relevant discussion boards. This is often an excellent way to quickly reach lots of interested people.
Send out a press release about the petition (particularly effective once you've collected a number of signatures)
Talk about the petition in online chat rooms.
Add a link to the petition in your email signature.
Add a link to the petition in your online newsletters.
Contact writers/journalists who write about the topic and tell them about the petition.
Add links to the petition on your web site.
Ask interest groups with large audiences to add a link on their website or in their newsletters.
Submit it to search engines (usually takes 3-4 weeks to be indexed - use the 'submit' tab at http://www.jimtools.com to quickly reach many search engines free).
Sign up petition signers for UCTP newsletters

Go beyond the petition:

Contact leading interest groups working on issues similar to your petition. Ask them how you can help them.
Organize school, neighborhood or other groups to brainstorm ideas and take action.
Make a donation to the group working on the cause!
Be a model citizen and Walk the Talk! As Mahatma Gandhi said so well, "We must become the change we want to see in the world"